[T. O'Heir]

Hi. You really need to narrow it down some. You thinking of shooting: Handgun? Rifle? Centre fire? Rimfire? All those but air powered? Shotgun? The Shooting Games(IPSC/IDPA/USPSA)? There really is something for everybody.
Best place is at a club that shoots NRA matches(NRA's site has a list) and go to a few. Do not worry about how well you shoot either. Everybody is new at least once and you're competing against yourself. Not the guy who has been doing since before.
The NRA is not the only sponsor though. There's CAS(Cowboy Action), ISS,(Olympic style bullseye), NSSF, CMP, etc., etc. All of which are guaranteed to be fun. You'll meet some great people most of whom will bend over backwards to help a new shooter including lending they rifles.