Describing spells and spellcasting

Build up, release & impact

Actions tend to have 3 main stages: the initial build up, the release and the impact of the action. So for a simple spell it could be energy building up in a wand, the wand shooting it to a target, and the impact of the spell on the target. Depending on the type of spell you're describing, focusing on one or more of these can help elevate the spell description and make it stand out from others. This is also an easy way to enhance the description from the plain and simple to the more interesting and immersive.

Consider the difference between "He casts a fireball from his hand and the cave nearly explodes upon impact." and "He stretches his hand backward as a ball of blazing energies begins to form within his palm. With one swift motion he flings the fiery ball into the cave. A second of silent passes before a massive explosion echoes throughout the cave's chambers and fire bursts out from within it, all but licking your face as it reaches out as if trying to desperately hold onto something before being pulled back into the darkness from which it came."

Is the second one a bit over the top? Possibly. I don't recommend going in such detail and length for every spell, but when the stakes are high or a moment of drama is called for, increasing the length of the description can be very effective. It's the same principle of build up, release and impact, except this time it's about the way a moment in game comes across to your players.

Small spells or non-dramatic moments don't need long, detailed descriptions. If anything, they can disrupt the flow of the game. Longer descriptions for these types of spells could be cut into pieces so you'll have a different way of describing the exact same spell. For example:
"You repeat the same motions you've repeated a thousand times over and a small, thin burst of purplish energy shoots from your wand into the lock. You hear the magical energies pulse within as the lock glows violet for a few moments before a clicking sound lets you know the lock has opened."
This one is fine for a dramatic moment, but in other moments it can simply be turned into:
"You shoot a purplish energy from your wand and unlock the door."
"With a quick flick of the wrist you unlock the door with your wand."
"You cast your spell and the lock glows violet for a few seconds before the door creaks open."

Spell components

Many tabletop RPGs have a spell system with components many people ignore, especially the material components. In general, spells can have requirements that range from materials used, line of sight, range, spoken words, movements and tools required to cast it. These can all be used to enhance the description of a spell, but I'm going to ignore line of sight and range here to focus on the 4 that allow for the most personalisation of spells.
For those systems without spell components and requirements you can simply make them up, it gives you all the freedom to make everything look as personalised and detailed as you wish.

Movement

The movement requirement is often nothing more than a character being able to move freely rather than being restrained, but we can use movement for far more to enhance the way spells are used and described. They're incredibly easy to use for personalised descriptions, like the difference between "Their gloved hand closes with a controlled motion.." and "Their fist clenches fast and with anger..". These could be the same motions for the same spell, perhaps even performed by the same character at different emotional stages. Either way, it gives more insight into the character, their state and potentially the type of spell cast.

Also consider using martial arts or dance forms to enhance the way spells are performed. This won't work for every spell and it requires some homebrewing, but it can make casting some spells incredibly satisfying. Avatar: The Last Airbender and Avatar: The Legend of Korra are perfect examples of using martial arts for magical actions. There's something incredibly satisfying about seeing a character stomp their feet to shoot up a rock from the ground before punching it toward their target, which could be a way to change a simple earth blast spell. Even changing a magic attack from a palm or fist to a foot, knee or elbow can make for a nice personal touch to the exact same spell.

Materials

Materials are a perfect way to use the build up stage of a spell as well as a perfect way to telegraph a specific spell is about to be used, which in turn can make for dramatic moments. Materials can be used to describe a transformation from simple material to spell effect, from build up to release or for an ultimate bad guy reveal.
For example, for the majority of the campaign the party may have fought a masked villain who would constantly use a few specific spells in a specific way. Perhaps a coin is flicked in the air in a specific way. Later down the line the party may meet a stranger they end up helping, only to eventually see him use that same spell in the exact same way.

Materials can also be used to personalise the look of characters more. Perhaps somebody with feather fall has a hat with feathers they use for this purpose or perhaps somebody carries a lot of little jars with all sorts of strange materials for a wide range of spells. Using some creative liberties here can be helpful. Spells that require cheap materials could simply be rewritten as requiring the same materials. This way the feather hat could be used for more spells in potentially dramatic ways for example.

Words

Another easy way to make a spell stand out is to use a different language as a type of command word, this works especially well for charming and domination effects. I recommend picking a language unknown by anybody in the group for the full effect as it keeps things immersive while still allowing you to easily translate the spells with something like Google translate.
The immersive effect can drop when using a language others know because many English spells sound ridiculous when translated (directly) to another language.

It can also be wise to stick to only a few spells for this purpose to make sure they stick with the players. If the elusive villain uses a mind control spell, for example, a moment like "She looks you dead in the eyes and says 'Ahy Ianao'." could be one of "Oh crap" for the players.

Tools

Tools are another perfect way to personalise spells to make them different in appearance while maintaining the exact same functionality. For example, a simple spell shield type of spell could transform into actions like:
"..and their shield encases itself in a radiant barrier.."
"..their wand traces a shield in the air. Immediately arcane energies begin to manifest within it.."
"..they clench one of their chained sigils within their hand and a corporeal version of the shield on the sigil begins to form in front of them.."

With some homebrewing you can add a whole lot of fun customized items for spell effects and descriptions. There's no reason a walking cane couldn't be used as a staff, for example. Or a scarf could activate into a magical whip through a spell like conjure weapon or even a snake through a conjure animal spell. Spell effect don't necessarily have to come out of thin air. Even tattoos could become tools for spell casting.

Bonus

Using any of these 4 elements has another added bonus beyond immersion, character design, and so on, which is the way spells will be telegraphed through the description process. It shows the players a spell is being cast, allowing them a more natural way to cast a spell like counterspell or use a different form of interruption, which in turn allows for a more unique way to describe this process.
That same coin flick from earlier could turn a moment of "Oh crap" into "Hell yeah!" with a successful counterspell that shoots the coin out of the air or duplicates it a hundred times or teleports it into the hand of the counterspell caster or simply makes it disappear. In short: these moments offer a chance for players to feel extra badass or extra troubled or any other emotion you wish to convey in a specific moment.

Language use

If you're struggling with describing spells in ways that make them feel realistic or a good fit for your adventure, a specific character or other element of your story, consider the language you use to describe your magical effects. Take a simple blast spell, for example, which could be described simply as "a powerful blast". But there are usually different types of blast spells (or there could be if you customize them visually), so playing with these elements can help make characters stand out, make spells seem varied and improve your describing skills as well.
To continue with the blast spell, if the type is already given (fire blast, ice blast, etc.), you'll at least have those elements to play with. But turning "a powerful blast" into "a powerful blast of fire" isn't that much better. A fire blast could be "an erratic, fiery rage", an ice blast could be "a translucent, glacial force", and an electric blast "a bright, vibrating current" when they impact their target.
If the spell type isn't given, you can give it any type of characteristic you wish, so go nuts with making them stand out and memorable, which in turn can make the character using the spell more memorable.

Language use also applies to different schools of magic. There are many specific words you could reserve specifically for necrotic spells or fire spells or mind control spells. The same goes for the type of spell is like a healing spell, a projectile spell or a rain of magical particles. If you struggle with this, having a small list of words you can refer to for specific magic types can be helpful.

Further customization

If you want to take things a step further in terms of personalising spells, simply changing the color or vibrancy of a spell can change a lot, as can the energy with which a spell moves or activates. The same way a person can act erratic, controlled, emotional or confused, so too can a spell reflect different natures based on the person who casts it.

With some schools of magic you can also skew the definition a little. Fire can be lava, necrotic can be corruption, ice can be glass, and so on. Some spells may have to be altered slightly though. If ice becomes glass there wouldn't be a cold effect for example, but it can be changed to a different effect as long as it doesn't disrupt a balance. If having a bleed effect would be more powerful than a freezing effect, perhaps consider a different change to make the spell stand out.

Prepare ahead

If you struggle with coming up with suitable descriptions during the game, prepare a short list of descriptions for often used spells or for important characters. If your players struggle with describing their characters' actions, they could create descriptions for their fanciest spells or perhaps all of them if they don't have that many to keep track of.
With a little time your describing skill will hone itself and it'll become easier to describe spells colorfully and with unique twists.

Preparation can be as simple as having a short list of adjectives and/or adverbs for each type of spell you'll encounter. Sort them by a main characteristic, it doesn't matter if it's by school (fire, ice, etc.), effect type (burst, rain, blast, etc.), effect (healing, destruction, etc.) or something else as long as you can make spells stand out a little and enhance the description of it and thus the way the story is being told.

Other tips

Finally, if you need more help or more ways to shake things up, take into consideration what spells do to the surrounding area. Surroundings are often what changes the most, so to keep descriptions fresh you can simply change up what you describe in terms of what is affected by the spell. This goes beyond things breaking or catching fire, it includes sounds that may echo against cave walls or within a mountain range, it includes noises that may disappear (like scared animals), it includes screams of panicked people in the distance, and so on. This helps build a more living world too.

Another tip is to mix up your words to make sure a fire spell isn't always described as energetic or fiery for example. I touched on this briefly in the customization section, but fire spells could be described as "having the heat of dragonfire", "like a rising phoenix", "roaring like a blacksmith's furnace" or "having the brightness of a star". A necrotic spell could be described like "smelling of a week old carcass", "looking like a thundercloud of noxious fumes", "spreading like a spiderweb of corruption" and so on.
These are often more difficult to think of on the fly, so it could be worth having a list of them for specific spells or spell effects until you feel comfortable enough to improvise them.

Finally, practice makes perfect. This could mean practicing it by playing a game, but it could also mean practicing on your own. Simply looking for fun ways to describe spells on your own will usually mean at least a few stick for future use.
Giving yourself a challenge can be a fun and helpful way to do this too. Perhaps finding the most outlandish description or picking a list of random words you have to use for a set amount of spells. There's plenty of possibly challenges, you could even include other game masters to have fun and learn from each other together.