"Ranks" don't exist any more. Before you go off anywhere, talk to the trainer you want to improve with. As you gain experience, you'll automatically train in that skill, and you'll get a message each time your skills improve. You'll never have any "saved ranks," unless you've never chosen any trainer at all or earned a lot of ranks in the library, and you don't have to return to town to train. You do have to go back to town to choose a different trainer. When you switch trainers, any "leftover" experience is transferred to the new trainer.
All training now costs the same amount of experience per unit of training, and the size of those units has been changed accordingly. So if you insist, you can think of getting "1/2 of an old Faustus" or "1/4 of an old Evus" each time your skill at those improves. You're probably better off just starting fresh and ignoring the old system, though.
You improve in a skill every time you gain enough experience, except that you'll never improve more often than every couple of minutes. If you earn a lot of experience all at once, either in the library or some other way, it will be applied gradually over the first few minutes you're out of the library. You should have plenty of time to switch trainers if you don't want to use all your experience on the same thing.
The folks who used to tell you how many ranks you had (Ankrus, Astra [formerly Astrus], and the rest) now remind you which trainer you're currently studying with, and tell you approximately how far along you are to the next improvement.
Compiled and edited by Pamela Greene <pamg@alumni.rice.edu>. Additions, corrections, and suggestions for this file are welcomed!