Thoroughly scrub the joint between the window casing and the surrounding frame, using a dry scrub brush. Blow off the dust.
Set a caulk tube in your caulk gun. Cut off the end of the tube at a 45-degree angle to make a hole about a quarter-inch across.
Slide a 3-inch nail into the hole to break the inner seal.
Press the tip of the tube to one end of the first joint between the casing and the frame. Hold the gun at a diagonal angle. Squeeze the trigger until the caulk comes out the hole in the tip of the tube.
Pull the gun slowly backward along the joint, squeezing the trigger consistently and laying an even bead of caulk in the joint. Continue to the end of the joint.
Wet your thumb and press it over the new caulk line, running it from end to end. Press gently, so it just flattens the caulk line without removing it.
Repeat the process for each of the remaining joints around the window. Cover all the seams where the window casing meets the frame, and where the frame meets the wall. The caulk should dry to the touch within 12 hours.