This project covers cutting coped joints for inside corners.
Use coped joints instead of miters for an inside corner. You might have difficulty fitting inside miters because the wall surfaces tend to give slightly as you nail the pieces in place. Thus a miter joint that looks perfect when held up for a test fit is likely to gap when nailed in place. A coped joint, on the other hand, accommodates such variations.
A coped joint is essentially a butt joint in which one piece of molding runs right into the corner. The end of the adjoining piece is cut to match the profile of the first piece and butts up against it. This is not as difficult as it may sound; coped joints are much easier to cut than they look, and they are fairly forgiving of inaccuracies. The principal tool used is a coping saw.
Even the pros don't cut perfect copes every time. The trick is to take your time and leave the moldings a little long to begin with so you can sneak up on the perfect fit by fine-tuning the cut.