On arrival at Tampa Airport note that the baggage reclaim, as with ticketing and check in, is split into the red and blue sections depending on which airline you have travelled with (see below for the list). 

You can't just cross from one to the other.  If you are heading for red area and need to be in the blue area, then go to level 2 and walk across the lobby area where you can take the stairs (or elevator) down to level 1 and reverse directions from blue to red.

Go to the Red area baggage reclaim if you have travelled with: Air Canada, Air Tran, British Airways, Cayman Airways, Continental, Frontier, Midwest, Southwest, Spirit, Ted, United, West Jet

Go to the Blue area baggage reclaim if you have travelled with: American, Frontelta, Freedom Airlines, Jet Blue, KLM, Northwest, US Airways

Once you have collected your luggage, you will find taxis/cabs, bus services and hotel shuttle buses on this same level, 

Car Hire/rental desks are also situated in this area and there are six major car hire companies located at the airport: Avis, Budget, Dollar, Hertz, Enterprise and Thrifty

If you are unsure about where to go next or how to travel into downtown Tampa then ask at the Ground Transportation Information kiosks.