It works like this:

You have a stock of magic. That magic has a stat-affecting value: Like say, Firex100 is Str+50, Mag+54, Def+30, and Luck+1 (which is isn't, I just made those up)
Then when you junctioned fire to str, it'd go up 50, magic would go up 54 if you junctioned it to it, defense woulf raise if you junctioned it to def. If you split your fire stock 50/50 between squall and quistis, then it might only raise strength 25 if you had it junctioned there.

There is no MP in the game-- You can cast as many spells as you have in your inventory

You can junction any spell to any stat, if you have a GF that'll let you do so. Shiva lets you junction to strength right now and vitality, right? And I really have no clue what quezacotl's good for, probably magic and spirit or something. And later, you can change the spell. It doesn't matter, it only raises your stats temporarily, if you remove the junctions, it'll go back to the base statistics. (You raise stats permanently by using the str+, Mag+, vit+, spr+, and hp+ abilities when your GFs learn them (when you get ifrit, get him to learn his str%+ abilities after boost, that way you can junction str+ earlier in the game. and generally don't level a lot, just enough so that you fight all the battles necessary to get all the spells. The more levels you have left over when you get the GFs bahamut and cactuar the better you'll be, because then you can raise four stats per level up)

All elements raise the stats equally, if they're of the same rank. Fire and blizzardx100 would both raise strength by 50 in my example about Stronger versions raise them more-- Firaga and Blizzaga might raise it by 100. (which they don't, but you get the idea) Just try all the spells out in the stats you can junction to right now to see what the best combination is

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A short summary:
Draw 100x spells every time you find a new one.
Don't level much,
To make an attack with an element, instad of just boosting strength, add it to the elem atk junction.
Look for the best combinations of junctions that gives you the best and highest balance of stats.