Mark each wall and measure the baseboard to fit. Mark cuts that require a 45-degree miter cut with an "M". Mark cuts that abut door trim "D" and cut them at 22 degrees so that they taper into the door for a finished look.
Find the starting point for miter cuts by laying the 1/4-round molding against the baseboard and marking the place where the molding meets the edge of the outside corner. Draw a freehand cut line in the direction of the cut from the starting mark. The direction of the cut will be obvious once the molding is laid out, and two pieces meeting at a corner will always form a 90-degree angle.
Place the mitered end of the first strip of 1/4-round molding in an inside corner, and lay the strip along the wall. The molding is relatively flimsy, so press it tight against the baseboard while nailing with the nail gun. Sink each nail head below the surface by hitting it with a nail set, if you are using a hammer. Fill the holes with wood putty.
Place 2-inch finishing nails every 12 inches through the 1/4-round molding so that the nails go through the baseboard and into the sole plate (bottom horizontal framing member). Continue nailing around the room until you return to your starting position in the inside corner. Finish by completing the other side of the miter joint.