To begin with, clean out the old grout. You may need to chip away at it. When done, spend a moment vacuuming out all the dust in the area. After you’ve mixed the new grout to the point where it’s not powdery at all, then you’re ready to apply it. Smear grout diagonally, pushing it into the joints. Sponge the surface with a damp sponge - rinsing and repeating until you’re left with a thin haze. Allow the grout to harden slightly, and then run the sponge over the grout lines, pressing gently into them to depress it slightly. When the grout is completely dry, polish everything with a microfiber towel. Just remember to be patient, and it will look professional.