Run the cable up behind your drywall. This will require cutting holes in your drywall so that you can connect the cabling to your studs or joists at least every 4 feet. Drill your holes in the middle of studs or joists so that you don't risk cracking them.
Use your drywall cutter to make a hole large enough for the subpanel. With sheet metal screws, connect the panel to the studs behind it. Then bring the cable into the panel, securing it into a cable clamp.
Connect the ground wire to the ground bus. Connect the hot wires to a lug on the bus bars and hook the neutral wire to the neutral bus bar. Hot wires are black and red; neutral wires are white; and the ground wire will be bare. Use a screwdriver to tighten the connections.
Bring the subpanel cable into the main breaker box. Connect the white neutral wire to the neutral bus bar, and the ground wire to the ground bus bar. Then hook the hot wires up to a two-pole circuit breaker suited for 50 amps.
Install the new circuit wiring you'll need in the subpanel. For each circuit, connect ground wire to the ground bus and each neutral wire to the neutral bus. Connect as many circuit breakers as you need to the panel; depending on the manufacturer, they usually just snap into place on the hot bus bar.