How to measure the size of a suitable tire for my bike?
Measure the diameter of the bead seat (i.e. the place where the tire bead will sit).  It will most likely be one of these:


559mm = MTB 26 inch tire.
622mm = 700C (a.k.a 29er)
630mm = 27 inch that is old enough to remember the Bee Gees.


If it's not one of those, look it up here:  http://sheldonbrown.com/tire-sizing.html#iso

The new tire will have a marking on it like 28-622.  That second number is the diameter.