The system for acquiring Magic in Final Fantasy VIII is very different from previous Final Fantasy titles and was not replicated in future games in the series. This is most likely because, truth be told, it can be an annoying system to deal with at times and it has some unintended draw backs that its unclear whether the game designers were considering.
Characters in Final Fantasy VIII do not have Magic Points (MP), instead your characters will need to use the 
Draw command to Draw magic from enemies or from Draw Points around the world.
This will allow them to stockpile spells and then use the Magic command to cast them in battle. They can also junction them directly to player stats. Check out the Magic Junction System section below for more information on how to junction magic:
The alternative to drawing magic from enemies and from using Draw Points is to refine items into magic spells. This can be done by using the following abilities:
F Mag-RF (Refine Fire magic from an item.)Forbid Mag-RF (Refine Forbidden magic from an item.)High Mag-RF (Refine High-Level magic from other Magic.)I Mag-RF (Refine Water/Ice magic from an item.)L Mag-RF (Refine Life/Recovery magic from an item.)Mid Mag-RF (Refine Mid-Level magic from other Magic.)ST Mag-RF (Refine status magic from an item.)Supt Mag-RF (Refine Support magic from an item.)T Mag-RF (Refine Lightning/Wind magic from an item.)Time Mag-RF (Refine Time/Space magic from an item.)The easiest method to do this is to utilize the Triple Triad Power Up Strategy. This will allow you to use the Card Mod ability to refine cards into items that you can then use the refine abilities above in order to turn into powerful magic that your character can junction.
As a result of the way that magic functions, unfortunately you will actually reduce your characters stats any time you cast a spell that you have junctioned to a stat.
In other words, having 100 
Ultima magic equipped to your Strength stat, followed by casting Ultima and reducing that to 99 Ultima magic, will reduce that character’s Strength. Pretty counterintuitive, no? Unfortunately, this means that actually using any of your magic is detrimental to your characters overall stats.
Make sure that you continue to use Draw to stockpile magic from high level monsters. Note that the highest level monsters you can obtain magic from are located on the Island Closest to Hell and the Island Closest to Heaven. Check out the links below for more information:
Finally, the maximum amount of magic that you can carry is 100 of each spell, and the maximum number of spells that you can have on any character is 32. You can free up some space by accessing the Magic menu, selecting the “Exchange” option and pressing the 
Button to discard spells.
Many of the lower level spells, such as Fire, Blizzard and Thunder, just end up taking space in your magic screen later on in the game, so feel free to discard them. Just make sure not to discard any important spells accidentally!
