CUT AWAY THE old caulk from around the top of the tub. Then thoroughly clean the joint of all grime, dust and soap buildup.
Two types of grout are commonly available: premixed and powdered. Easy-to-use premixed grout ($3 for a half-pint) works well for small repairs. Scoop some out of the container and press it into the seams between tiles with your finger.
For large regrouting jobs, buy a 5-lb. carton of powdered grout ($5) and a quart of liquid latex additive ($7). This make-it-yourself approach allows you to mix up fresh batches of grout as you need it.
Dump a cup or two of grout into a small, clean plastic bucket, and then pour in enough latex additive to hydrate the powder. You could mix the powder with plain water, but the liquid latex makes the grout more water-resistant and much stronger. Mix the grout thoroughly with a paint stirrer or putty knife. Add more powder or liquid latex if necessary until the mixture is the consistency of mayonnaise. Before moving onto the next step, let the grout sit for three or four minutes.
Use a rubber float (about $7) to force the grout into the joints (photo above, left). Push the float diagonally across the tile and be sure not to miss any spots. Wait about five minutes, then use a clean, damp sponge to wipe the excess grout from the tile (photo above, right). Rinse the sponge frequently in clean water and continue wiping until only a light haze remains. Allow the grout to set overnight, then buff off the haze with a soft, dry cotton cloth.