I'm no expert on this, but I would start with a bucket of detergenty water and a scrubbing brush. If it's just grime that you need to get off, that should do the trick.
However, if that's not intensive enough, have a look at this website - it's got some useful information on cleaning slate.
Liberon do a natural stone floor cleaner here "Liberon Stone Floor Cleaner is ideal for removing built-up layers of dirt, grease and Liberon Stone Floor Shine from previously sealed and unsealed terracotta and natural stone flooring"