Mitre-box saws are most often used for trimwork, and for a reason: Trim generally is installed with mitred (angled) cuts in the corners. A mitre saw is the only way to get that angle exactly right. If you want to install trim without a mitre box, however, there is a way to do it using only square cuts, which you can make with a standard circular saw. By using corner blocks to form your corners, you avoid mitring altogether.
Predrill four nail holes with your pilot bit in each of your corner-block trim pieces. Put two holes, top and bottom, all the way through the blocks in each direction. Offset the positions of the holes just enough so they don't intersect with each other.
Stand a block in one corner of the room. Set a small level alongside it and get it perfectly plumb -- straight up and down. Hammer trim nails through the two holes on each exposed side of the block into the wall behind it to secure it. Sink the nail heads with a nail set. Follow the same procedure to install corner blocks in each corner of the room.
Measure between two of the corner blocks, from the inside edge of each, using a tape measure. Mark the measurement on a longer piece of trim with a pencil. Don't measure from the end, as it might not be square. Make one mark a few inches in from one end of the trim, then start your wall measurement from there to make the second mark.
Mark straight lines across the trim at both marks. Set a try square along the edge of the trim to ensure the lines are completely square.
Cut the trim with a circular saw. Cut slowly and straight along both lines.
Set the cut trim between the two corner blocks, so the square-cut ends of the trim butt against the sides of the blocks. Drill pilot holes every 12 to 16 inches along the upper and lower edges of the trim piece.
Hammer in finish nails. Sink the heads below the surface with a nail set. Repeat for each section of the wall between all the corner blocks.