Note! This mission is optional and doesn't even appear in the journal, though you should repeat it from time to time, especially if you have excess Soul Gems and want to sell them for a good prize. You will get the chance to receive this quest no sooner than after finishing the first main College quest, First Lessons.
Find Sergius Turrianus (he's usually on the main square or at the Hall of the Elements) and ask if he doesn't need your help with anything. One of the missions that he might give you is bringing him a random number of Soul Gems of random quality (most of the time petty, lesser or common). If you have the right Gems, you can just give them to him. Otherwise you will have to search for them. I wouldn't recommend buying them, as it would make the whole quest pointless. It's much better to look around for them. Inside the College Gems can be found most of all inside mages' quarters, though in most cases you would have to steal them. You can also check the big light pillars found in the main areas of the College from time to time. In return for brining Sergius the gems, you will receive gold.