Take the easiest route when installing a new circuit by running it up to the attic, over and down to the breaker service panel. Drill a hole using a 5/8 inch bit, the size recommended in "Advanced Home Wiring" by Black and Decker, through the top sill in the attic above the dryer outlet and another above the breaker box. The top plate is the horizontal framing to which the wall studs attach at the top of the wall.
Run the end of a fish tape through the hole drilled above the planned dryer outlet down to the outlet opening. Attach the wire to the fish tape and secure it with electrical tape. Return to the attic and pull the wire up the inside of the wall, through the hole bored in the top plate and into the attic. According to the Meriwether Lewis Electric Cooperative, "#10/3 electrical cable is the most commonly used size for 220 dryer circuits and NM (non-metallic) cable is the most commonly used type."
Shut off the main circuit breaker before proceeding to cut off the power. Remove a knockout slug from the side of the breaker box using a screwdriver and hammer. Knockout slugs are circular metal discs that cover wiring openings to the breaker box until needed.
Run the cable across the tops of the ceiling joists to the wall where the circuit breaker panel is located. Feed the cable through the hole bored in the sill plate and down to the breaker box. Pull the cable through the hole where the knockout slug was removed. Secure the cable to the breaker box using a cable clamp.
Strip about 12 inches of insulation from the cable to expose the conductors and copper ground wire. Strip 1/2-inch of insulation from the three conductors. Attach the neutral (white) wire to the neutral bus bar. Attach the ground wire to the ground bar and the black and red conductors to a double-pole, 30-amp breaker.
Attach the remaining end of the cable to the dryer electrical outlet. Install the outlet in the wall and then restore the power. Check the installation with a circuit tester to verify that there is power to the outlet.