Furnace leaking water: where it comes from and what to do
Water under a furnace has exactly four sources. Which one depends mostly on whether your exhaust pipe is metal or plastic.
Condensate drain (high-efficiency, PVC exhaust)
Condensing furnaces make water constantly; it leaves through a small trap and hose. Algae clogs the trap, water backs up and out. Find the trap at the unit's base, pull it, flush it clean. Ten-minute fix, no parts.
Condensate pump
If the drain runs to a small box that pumps water up and away, that pump's float sticks or the pump dies. Pumps are ~$50 and swap with two hose connections and a plug.
The AC coil above the furnace
If it leaks in summer or the shared coil drain pan rusted through, water drips down onto the furnace. The furnace is the victim, not the cause — this is an AC-side repair.
Flue condensation (metal exhaust, 80% furnaces)
A conventional furnace venting into a too-large or cold chimney condenses exhaust that runs back down. Needs a technician to assess the flue sizing or add a liner; ignoring it rusts the furnace from the top down.
Is the furnace flashing a light?
If the burners will not light, the control board is almost certainly flashing a diagnostic code behind the little window. Count the flashes and look the code up by brand here — walking into the phone call knowing the code saves diagnostic time.