Installing baseboard is one of the easier facets of finish carpentry. By learning just this part of finish carpentry you will be surprised at how easy and fast you pick up the other aspects regarding trimming. In a sense it is the plat form or starting point to learning this trade. Of course installing doors and casing doors and trimming windows is a little more complicated but is not really that tough with a little research or guidance.
When you come to an inside corner there are a couple ways to handle these. One way is to miter the joint. The other way and most preferred is coping the joint. Coping is cleaner and neater looking and just plain easier. To start from the beginning for doing a cope read careful, you only cope one piece and that is the second piece that leads out of the corner.
The first piece of baseboard goes squarely and tightly against and into the corner. Then the actual cope goes onto the second piece of baseboard that meets the first piece that was previously installed. Take this second piece of baseboard and make a 45 degree back cut on the end that goes into the corner. On this piece there will be a natural cut line or profile line. Simply use a coping saw and cut off the material by following this natural profile line.
This will create the exact profile of the baseboard and this piece will fit exactly into the first piece like a glove. When you are cutting with the coping saw be sure to be creating a bevel so the back of the baseboard is slightly shorter then the face or front.