Fixing a Slate Floor?

I have a slate floor in my kitchen that was done by the prior owners. I like it fine, but a few of the slate pieces have come loose (one broke off in the corner although it is still there) and the grout seems to be disappearing. Any recommendatiosn for someone who would able to fix it? Its a pretty small job, so I’m not sure what my best bet is. Most of the florr repair stuff in the forums that I have seen is aimed at repairing/redoing wood floors.