Clean the area to be caulked, concentrating on both the marble tile and the surface that it meets.
Cut the tip of your caulk applicator at a 45-degree angle with scissors or utility knife. The tip should just fit the gap to be caulked.
Dampen both surfaces surrounding the gap using a sponge and water to make cleaning away any excess caulk easier.
Apply caulk to the gap, being careful not to apply too much. Try working a few feet at first until you get the hang of the process then you can do an entire length of a gap.
Dampen your finger and smooth the surface of the caulk. If caulk squeezes out of the gap, you know that you have applied too much caulk. Clean with water and start again.
Clean the area surrounding the caulk line using a damp rag. Be careful not to touch the caulk.