Lay a drop cloth on the tile floor.
Mix grout compound and water in a plastic bucket according to package instructions.
Pick up about three tablespoons of grout on the trowel and spread it over the tiles, making sure to push the grout in between the tiles. Scrape away excess grout with the trowel.
Allow the grout to set for about a minute.
Dampen a sponge and wipe away the excess grout.
Allow the grout to dry according to package instructions, typically overnight. In the morning you will see a white film on the tile cove base tiles. Wipe away the film with a clean, damp sponge.