The important thing to take away is that anything cold (glass of soda, can of beer, air conditioner evaporator (the "inside" part) is going to collect condensation. ESPECIALLY SO in florida (which is where you are, IIRC) That's your water source. So now the question is: why isn't the water going away?
if you have a window unit, then the talk elsewhere in this thread is relevant. If you have a split (central AC) unit with a fan that distributes cold air to each room, then you have a different situation; Yes, there could still be a rust-out problem, but it's more likely that the drain is clogged, or if there;s a "condensate pump", it's got plugged, disconnected or has otherwise failed, and the condensed water is finding another exit.
what to do?
First, have a look at Smoriso's first link. If your inside unit looks anything like that (it's probably not that exact model, but they don't vary too much from the overall look) then you have a central AC unit and the rest of this post makes sense. . . if not, others have covered the appropriate steps already.
Assuming a central AC unit: look for a plastic or copper pipe coming from the bottom of it somewhere. That pipe may have a p-trap like you'll find under a sink; if that's got full of bugs, dust, mold, rust, paint flakes, etc, ad nausium, then your first step is to correct that problem.
While you're in there, grab a nice, bright light and have a look at where and how the pipe runs- it should go to a sewer connection or a sort of bucket arrangement with a pump in it,
which then pumps the water to a drain or to the outside of the condo unit.
Check the condensate pump, if you have one- it might be jammed with a bug, etc, the float switch might be dead/maladjusted, the PUMP might be dead, or the power might have got disconnected somehow. Triage: open the cover, and lift the float all the way as far up as it goes.
If the pump starts, or tries to start, then either there's no problem or the problem will be obvious, if the pump doesn't pump. If no response at all from the pump, then you're chasing an electrical fault or a bad pump. If you can take the pump out, take it to a sink and plug it in; see if it works there. You can also try it in place with an extension cord. Pump pumps on alternate power? That implies bad power near the AC unit, and now you can either call an electrician or chase the electricals yourself (work safely!). (if bad power, I would suspect a bad outlet- cheap ones rust and fail, particularly in a high humidity environment like an AC closet) Pump won't work even on known good power? You've found your problem and can take appropriate steps. It's possible that the float switch is bad or badly adjusted, so check the pump separate from the float if you can.
Next, check the pipe for leaks while you're at it. Fix'em as you find'em. Insulating that pipe might help; it'll contain cold water, which will itself condense water on the outside of the pipe, which could be enough to feed a mold problem. Don't mistake secondary condensation for a leak, or vice-versa. Plastic pipe is particularly prone to cracked joints from the vibration of the AC unit, but a copper or steel line might have a crack or a pinhole, too.
Then, since you're dirty and annoyed anyway, take the covers off the AC unit and poke around with a long screwdriver and a flashlight, to see if there's a crack or rusted out spot in the bottom of the unit. As smorizo points out, turning off the power to the unit AT THE BREAKER PANEL is probably a good idea. There are a number of things here that could bite you. if you find a bad spot in the tray, then you're into something that you're probably going to want to discuss with a professional. . . . with whom you may also want to talk about insulating the unit and its ductwork if it's not already.