Measure over from the beginning corner 16 inches and make a mark, at both the top of the wall and the bottom, if you plan to install mainly vertical furring strips. Snap a chalk line or run a pencil and straight edge down the wall to mark. Continue across the wall, marking every 16 inches.
Mark 16 inches up from the bottom of the wall if you choose a mainly horizontal installation. Run a line across the wall to mark the furring strip location. In most cases vertical furring strips prove preferable as easier to install. However, when installing drywall over wiring, horizontal furring allows you to avoid the wires.
Lay a long carpenter's level -- at least a 4-foot level if not a 6-foot -- against the wall, along the furring strip lines you marked. Check for both level horizontally and plumb vertically. Make a mark at any locations that sink below the straight edge or high areas, as indicated by pushing the level up.
Install the footer furring strip, which runs horizontally along the floor line. Run a bead of construction adhesive the length of the strip before pressing it into place about 1/4 to 1/2 inch above the floor surface. Delay using the glue if this strip, or any other, covers a wall area that is not level or plumb.
Sand the furring strip or the wall, unless it is concrete or brick, slightly to bring a high spot down to the proper level before gluing the strip. If the strip covers a low spot, secure to the wall with a nail or screw on either end of the strip. Wedge enough shims behind the strip to bring it level with the wall surface. Check, using your level, following with adhesive squirted behind the strip, before pressing it against the wall to secure. Follow this procedure for all high or low areas you encounter.
Anchor each furring strip, whether vertical or horizontal, with nails if covering a wood wall and with masonry screws if the wall is concrete or brick. Drill through the strip, into the masonry walls, and insert the anchors and screws as directed on the product instructions. Space nails or screws 12 to 16 inches apart.
Attach the top furring strip, near the ceiling, similarly. Leave a slight gap of about 1/4 to 1/2 inch between the strip and the ceiling. Sand or shim if necessary. Glue and anchor in place.
Place vertical furring strips on either end of the wall, against the corners. Continue sanding or shimming only as needed. Allow a slight gap between the furring strips and the adjoining corners. Glue and secure.
Secure either horizontal or vertical furring strips inside the framework created with the footer, header and corner furring strips previously attached. Ensure you build up or sand down low and high spots as you attach the furring strips with glue and nails or masonry anchors.
Frame around any door or window openings similarly, placing vertical and horizontal furring strips, cut to size, along the outer edges. Check to ensure each is level and flush as you work.