Mop and bucket of very hot water plus a trace of detergent (Flash or similar) work wonders . I work in a pro kitchen with tiled floors and I have to clean it twice a day. Comes up spotless and dries in a few mins max. We have delivery men with muddy boots tramping all over it as well as the mess 3 chefs make.
Too much detergent makes it worse , leaves steaks and too many bubbles so does not dry as fast. Do not bother with a steamer, buy a decent mop and a bucket that will wring the mop almost dry , a wet mop takes longer and does not clean as well.
A good mop with very hot water small amount of detergent 10 to 20 ml to a bucket, then wring the mop as dry as possible , your floor will come up sparkling will dry in 2 mins or so.
If you have some ground in dirt you may need to give it a good scrub the first time or 2 to get it really clean to start with, but then a few min with a mop as suggested and it will be clean enough to eat your dinner off.