As far as the area of your yard that's currently pooling water, you need to dig yourself a french drain of sorts. Dig out a large enough area about 2 feet down. If it's 2 feet wide by 3 feet wide by 2 feet deep, this should be plenty. Connect the plumbing I mentioned in my previous post to the grave at the 18" mark. I'd then line the 'grave' with enough extra fabric to fold over the top of the 'grave' (when you're done). After the fabric is in place, fill the hole to about 4" from the top with 3/4" gravel. Then fold over the extra fabric (don't worry about the extra over-lap.) Then cover the remaining 4" with dirt / sod.
I'm a little excessive when it comes to water-related projects due to the ice storms in the NE back in 1993. What I did in addition to all that I mentioned was install a clean-out every 25'. Also, in the center of the grave, I actually put in a drain cap that's attached to a 12" piece of verticle black pipe, and set it in the middle of the grave about 1-2" above the sod. This way, as the water rises, it starts to run into the grave and doesn't spread all over the yard until it leaches into the grave's top layer of soil. (Whew!!!). You can set the drain to whatever height you want; the lower the better. If you do this, before you put the cap on, I'd lay a double piece of landscape fabric over the 'stack', and then put the cap on. This way, leaves and dirt and twigs won't clog your french drain. The gravel needs to be kept 'clean'. This is the purpose of the filter fabric in the grave and in the pipe you've run. You can get filter fabric at a gravel yard. I spent $75 for 300 feet. I only needed about half but I know I probably use it for something else in the future. If you know a contractor, perhaps they can get it for you at a discount.