Choose a location where you wish to discharge the extra water. This is ideally slightly downhill from the problem area and away from the house. Most municipal property rules won't allow moving water onto a neighbor's property.
Spray paint a line from the start of the wet area to the discharge point. This is where you are going to run the underground pipe. The line should run down the exact center of the wet area.
Dig a trench along the painted line, one foot wide and at least one to two feet deep. The trench should slightly slope down towards the discharge point.
Pour one to two inches of gravel in the base of the trench. This is called "bedding the pipe" and is intended to provide an ideal surface for the pipe to rest on.
Lay the pipe in the trench. Start at the high end, and roll it to the discharge point.
Cover the pipe with gravel up to one inch above the top of the pipe. Cover the gravel with a single layer of landscaper's cloth.
Fill the rest of the trench with the top soil you removed in Step 3 and lay sod on top.