Properly wiring a separate building's electrical circuits into your home's main service panel requires the installation of a sub-panel in the secondary building. The sub-panel feeds the power from the main service panel out to the various outlets and lights installed and connected to the sub-panel. Because this type of project can be rather complex, consult a licensed electrician if you have any questions.
Turn off the power to the main service panel. Remove the screws holding the service panel door and set the door and screws aside. Knock out one of the cable punch-out holes in the top of the panel box. Install one of the cable clamps in the punch-out hole and tighten it down using the screwdriver and pliers.
Locate the area where the sub-panel will be installed. Punch out a mounting hole in each corner of the back of the sub-panel. Position the sub-panel in place and screw it into the wall using the included screws and screwdriver to tighten them down. Punch out a knockout hole in the top of the panel. Install the remaining cable clamp and tighten in down in the hole.
Feed the 6-3 electrical cable up through the hole in the sub-panel and over to the main service panel box. Feed that end of the cable down through the hole in the main service panel and out the front. Leave about 2 feet of cable hanging free out of each panel. For more details on how to feed/run electrical cable underground from the two building locations and to the service panels, see the link in Resources.
Strip off 15 inches of outer sheathing off each end of the electrical cable. This will reveal four internal wires, three insulated and one bare. Strip 1 inch of insulation off each insulated wire at both ends of the cable.
Connect the 6-3 gauge wire to the sub-panel. Connect the bare wire to the ground strip and the white wire to the neutral bus strip. Connect the red and black (hot) wires to the two main screw lugs at the top of the "hot" bus strip running down the center of the panel. Tighten each screw down on the wire. Attach the sub-panel cover door and tighten the screws down holding it in place. Tighten the cable clamp down on the wire to hold it secure in place.
Locate an open slot in the main service panel to install the 50-amp double-pole circuit breaker. Install the breaker by pushing the two U-shaped clamps down on the two pins in the slot on the service panel. Tighten the cable clamp down on the wiring to hold it secure.
Connect the wiring to the 50-amp breaker. Connect the black and red (hot) wires to the two brass screws on the breaker. Connect the white (neutral) wire to the neutral bus strip running down the center of the panel. Connect the bare wire to the grounding strip. Tighten down the screws on each wire securing them in place.
Re-attach the main service cover panel door, by inserting screws into each hole and tightening them down. Turn the main power switch back to the on position.