The question title says it all: my mysticism is pathetic but I need to jack it up so I can use the soul-trap spell. How? And who trains in that field?

Go to the Imperial City and buy a low level detect life spell from Calandil at the Mystic Emporium (you can get the spell from some of the mage guilds as well). Repeatedly cast the basic detect life spell until your mysticism hits 25. Then, go buy a soul trap spell and you will be able to cast it.

Here is a listing of all trainers in the game. Just scroll down to mysticism: http://www.uesp.net/wiki/Oblivion:Trainers

You're better off buying a Mysticism spell you can use and start casting it all the time.

The game only allows 5 skill increases via trainers per level. Unless your're 5 points away from being able to use Soul Trap, there's no real point in doing it.

Are you able to use the Arcane University altars yet? If so, buy the cheapest Detect Life you can find and then go make an even weaker one at the altar just to use for self-training - e.g. 3 feet for one second, or whatever the minimum values are. Unless you're an Atronach, you'll regenerate the magicka as fast as you use it up casting. If you are an Atronach, still do it, but make a few Restore Magicka potions as well.

You can do the same with a lot of the 'cast-on-self' spells, such as a one-second bound dagger, or one-second shield 5% etc. to produce a spell that you can cast continuously.

I can't get into Arcane University yet because I haven't done the recommendation quest where I have to dive into the water and get the really heavy thing. I can't use the bouyancy spell on mself because my mysticism is too low. Seems a vicious cycle.

I'll get the detect life spell from Calandril.

Thanks for all your advice.

The other possibilities, to finish that recommendation quest, are to buy, steal or make some water-breathing potions, or to go talk to the old fisherman in Weye, just outside the main bridge from the Imperial City.

Yes go fishing. Weye is right west of the Imp. City. You can kill the fishes without staying too long underwater. Your reward will be a water breathing ring. I know what you'll tell to the fisherman afterward: Why didn't you gave it to me BEFORE!!!

Two points:

1) You can do the Cheydinhal recommendation without using the spell. There's enough time to go in and do everything (including the Nirnroot) before you need to breathe.

2) You don't need Mysticism for the Buoyancy spell, it's Alteration - both water breathing and feather are of that school.

Also, you needn't try to bring out the ring. Once you have it, and the quest advances, you can drop it again. Since time stops while you read the quest pop-up, you won't drown. A character with reasonable strength can drop their spare gear by the well before diving, and have the 150 encumbrance headroom to be able to move with it. If you picked a race/gender with only 30 strength, then dropping the ring may be the only option.