I just made a fantasy baseball account on Yahoo and I was wondering how many total players and how many of each position you get to draft for your final roster.

It depends on your league, but standard Yahoo leagues have 22 players. The starting roster is:

catcher
1st baseman
2nd baseman
3rd baseman
shortstop
3 outfielders
utility (a hitter at any position)
2 starting pitchers
2 relief pitchers
3 pitchers (starters or relievers)

Your bench spots can be divided as you choose between hitters and pitchers.