In a perfectly graded world, the land around your home would slope away from the exterior walls preventing flooded basements and crawlspaces. Then it would continue to slope to the boundaries of your property lines and miraculously disappear without ever causing a soggy back yard or flooding out your neighbors!
Alas, perfect grading is hard to find and thus we need a few creative solutions to help move things along. To move standing water out of a low lying area in your yard, a curtain drain works well. A curtain drain is a shallow trench dug to collect water from low lying areas and run it away via a perforated drain pipe surrounded by stone and covered by filter cloth.
To construct one, you'd dig a trench (maybe 12 x 12 ) just above the saturated area on the uphill side. The base of the trench should slope to a lower-lying area away from the area you are trying to dry out. Then, add about 2 inches of washed round stone or gravel (each stone should be 1 to 1 ½ in diameter).
On top of the stone, install a perforated PVC draining pipe. I prefer the 6 diameter PVC pipe and don't recommend the black plastic corrugated pipe that landscapers often use (it tends to crush easily). After the pipe is installed, make sure the end of it drains to daylight if possible to discharge the water away. Finally, add more stone to cover the top of the pipe, then cover that with filter cloth and top it off with two or three inches of soil. If built correctly, your soggy back yard wil become a thing of the past!