A damp sponge(rinsing the sponge in between wiping) repeatedly wiping the tiles until they are clean to the touch...
Dampen the grout you want to remove, as Nomad says, then use a razor scraper at a 45 degree angle if there is any that's too thick to remove with the sponge.. Don't know if this is the best way, but it is they way I remove dried grout from tiles. Not sure what you mean by (outside), of the tiles.
If you have removed a piece of tile and want to clean the grout off of the outside edges, you can use a small chisel.
If you have removed a piece of tile and want to clean the grout off of the outside edges, you can use a small chisel.