There are two approaches you can take: one is to drain the water away and the other is to open the soil up to let it soak in. Or I suppose you could build a pond under your fence ;-)

In order for water to drain away, you have to have a spot lower than the low spot you already have. Ideally the neighborhood would have been built with drainage in mind. And maybe yours was. It could be the previous owners have 'topdressed' every year and changed the way the yard drains. If your yard seems a little higher than the rest of the yards, then you might look for where the lowest spot is really supposed to be and remove all the soil blocking the original designed drainage.

Can you post a picture looking along the fence line?

You might be able to open the soil enough by spraying it with cheap shampoo. Use one that is clear. Spray at least 3 ounces per 1,000 square feet. You can go up to 30 ounces per 1,000 with no problems, but start with 3. What the shampoo does is reduce the surface tension of the water and allow it to penetrate between the soil particles that are holding it back. It's worth a try and usually works to soften soil. Apply several times giving it a week or two to show improvement before spraying again.