How can I get rid of standing water?

You could dig down where the water typically stands, and fill the deep hole with rock to make a french drain of sorts.

Hi ! I would dig a French and fill it with rock , so the water can drain away . Also look into plants that need a lot of water so they could naturally absorb the water . Willow trees are often planted in this type of area . Good luck !

I agree with planting Willow trees. If it's not a huge area another option would be to level it out by filling it in with a load of dirt so the water wouldn't pool in that spot.

Thanks a lot, How deep should I dig?

Thanks.

Yep agree I would dig down at two foot deep trench across the entire area where the water usually stands and fill it with rocks or bricks or whatever you may have on hand. If you don't have anything like that that would work you can purchase bags of rocks / gravel at your local hardware or home improvement store. Fill the trench nearly to the top and then cover it with dirt and sod - it will grow in really quickly and you'll never know its there but it should help a lot!