How to clean Terrazo floors with household products and ways to keep it clean?

To clean:
First (if it's clean) use a sealer to prevent stains.
Second, use neutral cleaners, neither acidic nor basic, to clean it. Basically, just use soap and water. A mop is commonly accepted, however, I don't see how using it in a swifer or something else could hurt, if you'd rather use that.

To keep it clean, a good sealer will help. Simply clean up any messes on it asap, and it reseal it occasionally, and you should be able to make it last.