I found this article online when attempting to fix my a/c unit that was leaking water in our garage (or basement). The text was pasted from the link below.
http://www.toad.net/~jsmeenen/drain.html
Air Conditioning Condensate and Water Leaks are easy to fix. Usually without professional help.
The problem is that dirt and crud will stop up the drain line and clog the pan. This will eventually happen to every system out there give it enough time.
While this problem makes a terrible mess and seems like to end of your system it is really quite easy to fix. Most system simply use a 3/4 inch PVC pipe to drain the water to a floor drain or sink. when (not if) this drain clogs the drain pan over flows (especially when the fan stops) and you have a mess.
Fixing this problem is rather easy. Simply take a wet dry vacuum and suck the drain line clean, 9 times out of 10 this will fix it and that is the last of this problem you will have for a few years. If the drain pan is really dirty then you will have to take the covers off the unit and vacuum it out. In extreme cases you may have to use compressed air, nitrogen or CO2 to blow out the drain line (expect a big mess at the other end).If you don't have either avaliable you can use the Garden hose to flush the line backwards (expect an even bigger mess on the other end)
In rare cases you may actually have a hole in the coil drain pan in which case the coil or the pan will have to be replaced especially if it is steel (but this is rare). In other rare cases we have had situations where grease or oil fumes from the furnace have condensed on the coil and caused the water to fall off the coil. When this happens you must clean the coil with soap or some solvent.
If the coil is totally stopped up the back pressure from the fan/blower can force the water out of the pan by undermining the bottom of the coil. When the coil is this dirty the coil usually needs to be replaced. You will also notice little or no air flow.
In most cases these condensate leaks are a do it yourself repair. Only if you must take the unit apart and can't, do you really need to call for help.