Wash the baseboard with a trisodium phosphate (TSP) solution. Rinse several times. Let the baseboard dry completely. Sand the baseboard with a fine-grit sandpaper so the paint will adhere. Rub along the sanded baseboard with a lint-free cloth to remove any dust.
Apply a strip of blue painter's tape along the floor to protect it, and make sure to get the edge of the tape evenly up against the baseboard. Also stick tape to the wall right up against the top edge of the baseboard. Press firmly on the edges of the painter's tape with a putty knife to ensure that there's a good seal. Use a drop cloth made of fabric on top of the rest of the nearby floor.
Dip the narrow, angled sash brush into the can of paint. Do not dip the brush any deeper into the paint than halfway up the bristles. Remove a bit of the paint on one side of the brush by tapping it lightly on the inside of the paint can's rim.
Draw the brush in long, horizontal strokes across the baseboard. Avoid getting a lot of paint on the blue tape as it can seep under the edges and leave a ragged line on the surface below the tape.
Overlap your new brush strokes a bit over the wet edge of your old ones to fill in paint where you ran out before, to remove any brush lines and to keep an even amount of paint applied to the baseboard.
Remove the tape at a slight angle while the paint is still wet. Discard the used tape, which will still have wet paint on it, with care. Close any cans of leftover paint and mark on them with a permanent marker the date and the name of the room that you painted. You may need touch-up paint in the future. Wash your brush with soap and warm water. Remove excess water after rinsing the brush, then let it dry completely before storing it.