Slate is very easy to clean using a normal hard surface cleaner or floor cleaner, the biggest mistake that a lot of cleaners do is to mix there solutions to strong, this only leaves residue on the floor and doesnt clean it any better or worse, make sure that you rinse the floor correctly to get rid of any possible residues.
Manufacturers of cleaning chemicals spend a lot of time and reserch into finding the correct dilution rates for there chemicals, so make sure you mix them correctly and it will make the job a whole lot easier.
regards Dave ADL