We have just purchased an older home and the shower in the master bath is leaking on the cold water side. I removed the screw in the middle and tried pulling the handle off with no success. I tried looking into and putting a flat blade screw driver in where the screw came from thinking that it could have a latch holding it on, no success. It does not have any small screw or anything else visible that is holding it on.

Any idea's?

Is this a two handle faucet or a single handle faucet. If it is a two handle you can buy a handle puller, it works with two arms that hook the back of the handle and a screw type stem that goes into where you took out the screw out of the handle. As you screw the stem in it pulls the handle off.
If it is a single handle but the screw back in that you took out of the handle but do not screw it all the way in, leave it about three turn from tight. Then have someone help you for this. Put a screw driver into the screw and while someone else pulls out on the handle you hit the back end of the screwdriver with a hammer, just easy taps, eventually the handle will break loose and then you can unscrew the screw and take the handle the rest of the way off.

Letmetellu is definitely on the right track. You need to describ your valve(s) as best you can. We need to determine if this is a valve or a cartridge.