If you are lucky enough to have you own boat you can launch it at the following places in South Tampa.
Picnic Island has a nice boat ramp and plenty of parking. The boat ramp is set at a fairly shallow angle so you may have to back your truck all the way into the water. You can get to anywhere in the bay pretty quickly from this ramp.
Gandy Park is a great boat ramp if you want access to Old Tampa Bay and the bayside Pinellas shoreline and flats. This is the best boat ramp in Tampa. It gets busy but it has bathrooms, boat wash area, fish cleaning areas and there are two bait shops just up the street. There is a fee and you can pay with a card. If you are coming from out of town this is probably the ramp for you.
Ballast Point boat ramp gives you access to Downtown and Tampa Bay, but you might not have anywhere to park your tow vehicle if you show up after 10am. If you plan on using this boat ramp, you should claim a parking spot before you launch. This park is often busy and cars will park in the boat/trailer parking area.
Seaplane Basin Park has two boat ramps. I suggest using the one on the Channel as it is the better of the two. This will give you access to Palm and Alafia rivers, beer can and fantasy island, as well as Downtown and the Hillsborough river.