Cut quarter round molding at 45 degrees in order to fit into 90-degree corners using a miter saw. For accurate miter cuts, clamp your work piece against the guide fence, ensure precise angular alignment of your miter saw, and make a slow, controlled cut through the work piece. For corners that don't measure 90 degrees, cut the molding at half the angle of the corner. For example, if the corner is 120 degrees, cut the molding at 60 degrees.
If you do not cut the miter perfectly, it creates a gap. Mitigate this problem by coping. Install the first length of molding so that it butts against the perpendicular wall. Place a piece of molding upside-down on a miter saw, so that the edge that will be against the wall is against the guide fence. Set the saw to 45 degrees. After the miter is complete, highlight the edge using a pencil or China marker. Use this line as a guide, and cut along it with a coping saw. Be sure to bevel the coping saw back at approximately a five-degree angle away from the profiled face of the molding. This ensures that if you create a gap, it's hidden behind the joint where it is not visible. Check the fit of the cut against the previously installed molding. Abrade small gaps protrusions using a rasp or sandpaper. Once you achieve the desired fit, install the baseboard.