Obtain an electrical wiring permit from the city building permits department. The National Electrical Code (NEC) allows a homeowner to do everything that a licensed electrician can do. The homeowner must perform the work in the same manner, as well as obtain a permit and have the work inspected.
Mount the sub-panel in an area of high-load concentration. Anchor it to the wall using the mounting hardware that came with the panel. You may mount it inside a cabinet or closet to conceal it as long as access to the panel will not be blocked. The NEC requires that a panel be easily accessible at all times.
Run the feeder cable from the sub-panel to the main breaker panel. The easiest way to do that is to run the cable down into the basement or crawlspace, then over and up to the main breaker panel. You can run the cable along the sides of the joists or through hole drilled through the joists. Secure the cable to the sides of the joists with cable straps. Cut the cable long enough to reach the top of both panels.
Remove one of the knockouts from the bottom of the sub-panel box. Drive the knockout in with the hammer and screwdriver and grab it with the wire cutters. Wiggle it back and forth until it snaps off. Install a cable connector in the hole.
Push the cable through the connector and secure in place by tightening the clamping screws. Remove the cable's outer jacket with the razor knife. Connect the red and black wires up to the panel's main lugs. Cut them off as needed and strip 1 inch of insulation from their ends. Slip the stripped ends in the lugs and tighten the compression screws down on them. Connect the white neutral wire to the panel's neutral bar and the bare ground wire to the ground bar in like manner.
Turn on the battery-powered work light and turn off the main circuit breaker. Remove the breaker panel covers. Proceed with caution because the wires bringing the power into the main breaker panel are still hot. Remove a knockout from the bottom of the panel and install a cable connector.
Install the new two-pole breaker in the panel. Depending on the panel that you are working with, the breaker may snap into place on the Buss bars or may be secured to the Buss bars with screws.
Run the cable through the cable connector, secure in place and strip as you did on the sub-panel end. Connect the red and black wires to the circuit breaker screw terminals. Connect the white and bar wires to the panels neutral and ground bars, respectively.
Arrange to have an inspection by the city building department. Once the work is approved, close up the panels and turn on the main breaker.