Buy a .22long rifle handgun, take it to the range and shoot it.
Get instruction and follow the advice of the instructor while you shoot the gun some more.
Join a club that has competition.
Learn how to compete and use that knowledge to shoot the gun some more.
Pick from the following .22lr handguns.
Ruger MK II or III
Browning Buckmark
Beretta NEO
Smith and Wesson 22a
There are of course many more handguns to choose from, but any of these will get you started.
It's fun to learn lots of stuff about guns. It's more fun to shoot them.
Oh and this site.
http://www.corneredcat.com/Contents/