Mark the outline of the new room on a basement or other floor. Get the corners square by measuring diagonals until they are equal and mark the location for base plates by snapping a chalk line along the inside edges of the walls to be added. Work from an existing wall; most added interior rooms will connect to at least one existing wall. Measure the height from floor to ceiling with a tape measure; remove any flooring or ceiling covering at the new wall locations first.
Choose one of two ways to build new walls. Nail base plates to the floor and top plates to ceiling joists and toenail studs to them by driving 16d framing nails diagonally with a hammer. Or build walls on an existing floor, slightly shorter than the height of the space so they can slide between floor and ceiling. Erect them and drive tapered wooden shims under the base plates at stud locations to lift the walls tight between floor and ceiling.
Space studs in new walls on 16-inch centers by marking an end stud on both top and bottom plates and measuring 15 1/4 inches in from that end to mark the second stud. Measure 16 inches from that line for the next stud, then another 16 inches and so on to the end of the wall. Mark another end stud 1 1/2 inches in from the other end of the wall.
Use a framing square and level to make sure the new walls are square and plumb when erected. Nail top and bottom plates to the floor and ceiling. Use 16d framing nails for the ceiling joists and concrete nails for the base plate on a concrete floor. Nail the corners of the room together with framing nails.
Frame any door openings by eliminating one stud at the door space. Cut a 2-by-6-inch board the width of the door opening and nail it level horizontally at the top of the door to the studs on either side. Cut studs with a circular saw to fit from the bottom of the header to the floor to support the header and nail them to the header and to outside studs on both sides. Install short studs to fit on 16-inch centers between the top of the header and the top wall plate.