What do I need to do to clean/restore these floor tiles?
The traditional way to seal the tiles and add a new sheen to the tiles is with Boiled Linseed Oil. These tiles are likely quarry tiles rather than the more modern replacement terracotta tiles. 

You can buy modern products that do that same job.

See this link https://lubelska.co.uk/how-to-seal-a-reclaimed-brick-or-terracotta-floor/