Soak the tube of caulking in hot water in a sink for 30 minutes before using the caulk. Because caulk stiffens when the weather is cold, it is more difficult to work with if you try and apply it directly without warming it. Hot water from the tap is sufficient, and you can fill the sink and let the tube sit, or you can run the hot water over it.
Note the size of the joint you need to caulk and check that against the tip of the tube. Most caulking tubes have pre-marked lines on the tip for where you need to cut the tube off with a utility knife. Cut the tube along the appropriate line. If there are no lines, you can trim down the tip manually. The goal is to have the tip just small enough to fit into the top section of the joint, but not so small that it goes down into the joint more than a 16th of an inch.
Insert the tube of caulking into the caulking gun. Take a damp sponge and wet the tile down around the edge of the joint to keep the excess caulk from sticking to the face of the tile. Press the tip of the caulking tube into the joint and pull the trigger on the gun. Fill the joint full and move the tube along the joint as you go.
Press your finger against the joint and run your finger down it to smooth the caulk and remove any excess. Wipe down the joint with a sponge, but only use light pressure. You do not want to remove the caulking from the joint, just clean any excess from the face of the tile from when you were smoothing it down with your finger.