Turn off the circuit breaker that controls the air handler.
Locate the end of your air handler's drainpipe. Attach the hose of an industrial wet/dry vacuum to the end of the drainpipe via a vacuum hose reducer small enough to insert into the drainpipe. If you cannot find one, use your fingers to close off the space between the exterior of the vacuum's hose and the exterior of the drainpipe to facilitate suction. Turn the vacuum on for a minute or so to suck any algae clogs out of the drain hose.
Look along your air handler's condensate drainpipe for the stem and cap that protrudes up from the PVC piping. This stem should be a couple feet away from the unit itself and easily visible.
Pull the cap off. Place a funnel in the stem and pour roughly one cup of bleach into the drainpipe to kill any algae buildup that may continue to clog the drain. Replace the cap.
Check the condensate pipe's connection. Make sure there are no gaps that would allow water to leak out. If you find a gap, simply shift the drainpipe back into place.