Diagnosis
Leaks usually come from loose connections or cracked filter sump housings. The most common spots are the quick-connect fittings and the O-rings on the filter housings.
How to Fix It
Dry everything thoroughly with a towel. Turn the water back on and watch closely. Start at the top where the water line enters the first housing and follow the path. Pay special attention to the white quick-connect fittings—push the tubing in firmly until it clicks. If a housing is leaking at the seam, turn off the water, remove the housing, and check the O-ring for nicks or debris. Clean it, lubricate it with a tiny bit of silicone grease (food-grade), and re-tighten the housing.
If That Didn't Work
Check the drain line connection at the saddle valve or the air gap faucet (if you have one). A loose drain line clamp can cause a slow drip that runs down the cabinet.
Heads Up
Don't just crank down on the plastic filter housings with all your might to stop a leak. You'll crack them. The seal is made by the O-ring, not brute force.