Look here - pretty much everything you need to know - http://www.parktool.com/repair/readhowto.asp?id=75
Pulling the cable moves mech to outer / big ring, so if mech won't change onto small ring suggests there is too much cable tension or cable is sticking.
Other possibility is that the low limit screw on the mech is not allowing it to move far enough inwards, regardless of tension.
1) Clean cables
2) Check inner position of mech cage, if not far enough turn low limit screw (inner one on top of mech) anticlockwise a quarter-turn at a time.
3) Ease cable tension by turning adjuster on down-tube or shifters (depending on your setup) clockwise a quarter-turn at a time.
Tip - small adjustments, and remember how far you turned things......