Attach this octagonal box(surface mount) to the wall in your garage near the existing outlet.

http://www.homedepot.com/webapp/wcs/stores/servlet/ProductDisplay?storeId=10051&langId=-1&catalogId=10053&productId=202056160

Use the rear knockout in the box and run new cable to the existing outlet to grab your power.

Then ceiling mount this box near the garage opener:
http://www.homedepot.com/webapp/wcs/stores/servlet/ProductDisplay?storeId=10051&langId=-1&catalogId=10053&productId=100538643

Run conduit from wall mounted box to ceiling mounted box.
Run individual wires from wall mounted box thru conduit into ceiling box and attach to duplex receptacle at ceiling.

Attach this cover plate at ceiling box:
http://www.homedepot.com/Electrical-Electrical-Boxes-Conduit-Fittings-Covers/h_d1/N-5yc1vZbohm/R-100038014/h_d2/ProductDisplay?catalogId=10053&langId=-1&storeId=10051

Personally I'd take down the extension cord when I left and let the new owner decide how he wants to power the garage door opener.

If you want to run on the surface, you need to provide physical protection for the wires which means some kind of conduit. You can use metal or plastic conduit depending on what your local codes allow. You can run non-metallic cable (aka Romex) inside of conduit for physical protection but it's typically easier to pull individual wires.

There are box extensions that allow you to "come out of the wall" using the existing junction box. On example I found quickly:
{{!gwi}}

From there just come up the wall, across the ceiling, and surface mount your new box. The conduit needs to be properly supported as well. Use a stand-off clamp if you don't want to get into bending offsets for the boxes.

As for wire size, you need to look at the circuit breaker. A twenty amp breaker will require 12 gauge wire and a 15 amp breaker 14 gauge wire.

Thanks, guys. Now I'm sure I can do it.