how do you determine tire size range for your rims

I'd like to put the narrowest (with the least tred) tires I can on the bike I have right now using the rims that are already there. How do you determine what that size would be? Is there a formula? a chart? I have already gone down one size narrower and I remember the guy showing me an even narrower tire (I think my response was ...eeeek!....at the time, but I'm ready now) I'm also ready to do this myself. ;) Also, any recommendations on online sites to buy tires from? - I'm just trying to get a little more speed and less friction for now. Shopping for a new bike - don't want to rush the decision. thanks so much.....:D

Sheldon Brown has a formula and charts. See http://www.sheldonbrown.com/tire-sizing.html