Paint both walls. If one paint color is a lighter shade than the other, like white, paint that wall all the way into the corner. Don't worry about getting the lighter color on the other wall. Allow the paint to dry.
Tape the corner, beginning at the top of the lighter colored wall. Pull the tape downward, keeping it taut while pressing it in a straight line against the corner. Continue on to the floor with a single piece of tape. Run your fingernail down the inside edge of the tape to seal it tightly against the wall.
Paint the corner with the lighter color, painting over the inside edge of the tape. Don’t worry about getting a little paint on the other wall. This will seal the edge of the tape. Allow the lighter colored paint to dry for 1 to 2 hours.
Paint the darker color in the corner. When the paint is dry, remove tape.