What's the best way to clean an old vinyl kitchen floor?

Once a month I use one cup of ammonia to two gallons of hot water and a few squirts of Dawn dish liquid. It removes old dirt, grime, and wax. Every week I use Dawn dish liquid and hot water.

Honestly? Best done the old fashioned way...a bucket of good hot water with ammonia in it, down on your hands and knees with a good scrub brush. Once you've got it good and clean rinse it with a clean bucket of hot water. Let it dry well and apply a coat of wax to make it shine.

I use a gallon of hot water mixed with a cup of vinegar and a tbs of dish soap. I do it the old fashioned way, on my knees using a rag so I can get into all those little corners. If the space is huge, or you have bad knees, definitely use a sponge mop. Then I do a quick mop up using hot water and 'blue' pinesol, it has a wonderful scent. Best of luck.

Yep, hands and knees scrubbing with hot water and ammonia.

I switched to using my carpet cleaner, and it does a great job. I put spic and span in it with hot water. I have also used lemon ammonia to get off the old wax.