Remove old grout with a grout saw, oscillating tool, or carbide scraper
Vacuum and clean the joints thoroughly
Let the tile and joints dry completely
Mix new grout according to the package instructions
Apply grout diagonally across the joints with a grout float
Press grout firmly into all joints
Remove excess grout from the tile surface with the float
Wait for the grout to set slightly
Wipe the tile with a damp sponge in light passes
Rinse the sponge often and change water as needed
Let the grout cure for the recommended time
Buff off any haze with a dry cloth
Apply grout sealer if required
Avoid using the area until fully cured