The base molding is usually one of the last architectural details installed in a room. Before you install your base molding, install your other vertical molding elements, such as window and door casings. Paint your walls after you install the molding, which is when you should also paint your molding; however, if you're staining, complete that part of the project before attaching the molding to the wall.
You'll need to splice your base molding whenever you don't have a continuous length of molding long enough to span an entire wall. When splicing, instead of using a "butt" joint where both piece's flat edges butt up against each other, cut the pieces at matching 45-degree angles, which allows you to drive nails through both pieces at the same time and creates a smoother, more professional looking splice. Always place base molding splices over a stud for a stronger hold. To avoid splicing your base molding, purchase only moldings longer than your wall; but that isn't always possible for rooms with walls longer than 16 feet, and longer pieces may warp over time.
Cutting corners with a miter box works well most of the time for outside corners, but inside corners are seldom exactly 90 degrees. Run one of your board's flat edges directly against the wall. "Cope" the other piece to match the first piece's profile, and then attach it directly to the face of the first piece.
You'll work a lot more quickly with more satisfying results if you don't use inferior tools. Instead of a hammer and nails, use a compressed air nail gun to avoid denting the wall or base molding with your hammer strikes. Coping your inside corners is possible using attachments to a jig saw, but most DIY home improvement sites, such as the Bob Vila website, recommend using a coping saw. Buy extra molding so you don't have to make a separate trip to purchase more due to a few uneven cuts or miscalculations.