Begin by clearing everything from the cabinet under the kitchen sink to give yourself ample room to work. Lay down old towels or rags on the cabinet floor to absorb any water that will inevitably spill. Put on your safety glasses to protect your eyes from splashes and a pair of rubber gloves to keep your hands clean and protected.

Boil a full kettle or a large pot of water. Once boiling, very carefully and slowly pour the entire amount of water directly into the clogged drain. Pouring slowly gives the hot water time to work on melting the solidified grease. Wait about 10-15 minutes, then test the drain with hot tap water. If the water starts to drain, even slowly, repeat the process with another pot of boiling water to flush more of the grease away.

If boiling water didn't work, the next step is to use a plunger. For a double sink, securely block one of the drains with a wet rag or a sink stopper. This ensures all the pressure is directed at the clog. If you have a garbage disposal, you will be plunging the disposal side. Fill the other side of the sink with a few inches of water to create a good seal around the plunger cup. Place the cup plunger over the drain, press down to create a seal, and then vigorously pump up and down for 20-30 seconds. Pull the plunger away quickly to see if the water drains.

If the clog persists, it's likely concentrated in the P-trap (the U-shaped pipe under the sink). Ensure your bucket is positioned directly under the trap. The trap is held in place by two large slip nuts. Loosen these nuts by turning them counter-clockwise. They should be hand-tight, but you may need channel-lock pliers for stubborn metal nuts. Once loose, gently wiggle the P-trap free and lower it into the bucket, draining the trapped water and gunk. Take the trap to another sink or outside and clean it thoroughly with a bottle brush, a bent coat hanger, and hot, soapy water. The clog is often a solid mass of greasy sludge that you can pull out.

If the P-trap was clean or cleaning it didn't solve the problem, the clog is further down the line. With the P-trap still removed, insert the end of a manual drain snake (or auger) into the drain pipe that goes into the wall (the stub-out). Push the snake in until you feel resistance. This is likely the clog. Tighten the setscrew on the snake's handle and turn the handle clockwise while simultaneously pushing forward and pulling back slightly. This motion will either break up the clog or hook onto it so you can pull it out. Retract the snake, clean the end, and repeat if necessary. You may need to feed out several feet of cable.

Once you believe the clog is cleared, carefully reassemble the P-trap, making sure the slip nuts are properly threaded and the plastic washers are seated correctly. Hand-tighten the nuts firmly. Place your dry towels back under the reassembled trap. Turn on the hot water tap and let it run for several minutes. Watch all the connections you touched for any signs of dripping. If you see a leak, you may need to tighten the slip nut a little more (no more than a quarter-turn with pliers). Once you've confirmed the drain is flowing freely and there are no leaks, you can clean up your tools and put everything back under the sink.