Blend your grout mix with water in your empty paint can. Follow the manufacturer's instructions for specific recommendations for mixing.
Allow your grout mixture to sit for about 15 minutes as it solidifies slightly, and becomes more firm. Firmness is important when plugging gaps with grout, as the grout will have the structural strength to remain in place, and will not run out onto the floor. Mix the grout one last time in preparation for application.
Put on your latex gloves, and scoop a bit of the grout mixture into your hand. Press the grout into the gap beneath your toilet base with your index finger. Spread it along the seam so that the fill is uniform. Continue the process around the entire base.
Allow the grout to dry for at least two hours, or as long as the manufacturer recommends. Use your wet sponge to remove the excess grout from the tile floor, and the toilet base. The result should be a clean, and even seam along the bottom rim.