Margaret, You certainly have my empathy as I have been attempting to replace my kitchen molding - half of it having been removed to replace the ceiling tiles after a rewiring job and adding new light fixtures and a fan. Each piece has required 3 cuts - the basic length, and then the 45 degree angled cuts. These made with the molding angled into the floor of the miter box and then the saw in the compound slot. One thing I became acutely aware of was that regardless of how well I had managed to cut those angles, I still needed a sharp knife or a coping saw. These allowed me to "fine tune" that original miter cut for a better fitting corner. The next secret that probably nobody has told you is that you use chaulking when you have the pieces tacked up on the corners to "even out" their appearance! It's a good idea to paint your milding before you start ... you can always touch it up later, and use a punch to tack the your nails in under the wood with a small dollop of paint over them they will never be noticed.
If your hands/arms/shoulders are not strong, as mine aren't (and I really learned the hard way), take your time and put up just a few pieces at a time.