How can I clean the ground in crud from a linoleum floor?

One cup of ammonia to one gallon hot water and a few squirts of Dawn dish liquid. I use it once a month for deep cleaning my vinyl floor and remove old wax. Open windows the odor is strong.

a steamer works really well and no fumes

A pair of knee pads, hot soapy water, and a large scrub brush. Even at that, this may not be possible to remove if the surface is worn out. If you manage to remove it, consider applying wax or a sealer of some sort.

You could try some Krud Kutter. But, if it is too ground in, and has penetrated the outer layer, it will be next to impossible, as it is embedded into the vinyl. Suellen ^^ is right.

I use my carpet cleaner and spic n span with hot water in the water tank. Tough spots I pour a bit of straight spic n span on it, then go over with the carpet cleaner. I hate those embossed vinyl floors.