Mastic is the glue that adheres the tile to the wall, floor, backsplash or whatever project you may be tiling. Mastic is best cleaned while wet and can be easily accomplished with only a damp cloth. However, if there is dried mastic left on a tile project this can prove to be more challenging and will need to be completely removed from the face of the tile before grouting.
Use the damp cloth to wipe away all excess mastic from the face of the tiles.
Remove all mastic that has squeezed up between the tiles and is protruding on the top edges of the tile with a damp cloth
Clean any remaining mastic residue with a damp cloth.
Use a putty knife or similar scraping tool to carefully scrape away all mastic from the tile. When scraping mastic from the edge of the tiles, be careful not to pry the tile loose.
Use a shop vac to vacuum away the dry mastic debris from between the grout lines.
Wipe away any mastic residue left behind.
If you will be working on the floor, knee pads can provide extra support for your knees. Regardless, if the mastic is wet or dry only remove the mastic that is protruding above your finished grout line. When wiping away the wet mastic, be sure not to move the tiles from their placement which will misalign your grout lines. If purchasing a putty knife, it doesn't matter if it stiff or flexible, either will suffice.