quote:
French drain is your best bet. It can be done fairly inexpensively if you are willing to dig it and install yourself. You can buy 10 ft sections of 4" pvc pipe and drill holes along one side of it. Put down a bed of gravel in bottom of trench, Wrap pipe in drain cloth (holes facing down) then cover with gravel. You can then cover back with dirt/sod or jut fill in with rock. Either way should work fine. Just make sure you slope the trench a bit to prevent standing water and have a good exit point for the discharge.
This is very much the correct answer. It'll probably cost ~$500 overall and take 1 or 2 days. I'd suggest a few tweaks:
1) Go outside right now, while it's till full of water. Put 3 stakes into the ground (north, middle, south), and run a string line at exactly the water elevation right now. This will give you a perfect level line to measure down from.
2) Rent a trencher. Get one with a 12" wide bucket, and dig an 18" deep trench that in the middle of the low spot, extending a few fee outside the fence. You'll need the pipe to go out to the curb in front.
3) Put down a layer of geotextile fabric, then put in 2-3" of pea gravel. Measure down from your level line so that you can tell it drains the correct direction. Rake it until it drains. ie: 8" deep at the high end, 12" in the middle, 16" at the low end.
4) Drop in one of these guys on the high end:
http://www.lowes.com/pd_508023-676-L1200DGGKIT___?productId=50053663&pl=1&Ntt=catch+basin . In later years, you're going to need this to run a shop vac through and pull out all the sediment when the drain gets clogged (ALL French drains eventually gets clogged). Mine doesn't have one, and I wish I'd have done it.
5) wrap a perforated 4" HDPE (or 4" PVC as SouldSlave describes) with holes in it in the same fabric, and drop it in. If using cement, you'll definately want to actually glue the pipe.
6) Fill the rest of the trench with pea gravel, and then wrap that geotextile fabric over the top, like this:

7) cover with a square of sod.
8) Every other year, pop the top off of your catch basin and vacuum the silt out of the bottom.