Identify a path for underground drain pipes. Plant stakes in the center of low spots. Lay a rope down in from the furthest point to the drainage outlet is the straightest route possible. If the main route doesn't run through every low spot, lay additional ropes from these spots to connect to the main rope.
Dig out a drainage canal 8 inches wide and 1 1/2 feet deep along the main and secondary paths. Slope the main path with a shovel so it has a 1/4 inch decline every foot of length towards the drainage outlet. Dig the same slope into the secondary paths to direct water to the main drainage trench.
Fill the bottom of the canals with 6 inches of gravel. Lay a bubble level on different sections to check the slope and shift the gravel as necessary.
Set 4-inch perforated drain pipes in the canals with the perforations turned to face the sky. Use elbow and "T" connectors to attach the pipes, pulling a drain sock over each section as you work to protect the pipes from small particles of debris.
Shovel another 6-inch-thick layer of gravel over top of the pipes. Roll strips of geotextile fabric over the top to stop debris from penetrating.
Stir compost and sand into the soil you removed to dig the trench. This adds oxygen and good bacteria, improving its composition and making it easier for water to penetrate through to the drain pipes.
Seed exposed dirt with Bermuda grass or another water-tolerant grass.