This sounds like a major project, so I suggest you contact a local expert to help you develop a plan, particularly because drainage is such an important factor. You want to make sure that your landscape design and plants are suited to the site, and also that any changes you make won't cause long-term problems for your home's foundation or for your neighbors.
Avoid trying to add more soil to change the drainage yourself without thoroughly studying the situation. Making a poorly thought-out change could end up costing you much more in the long run. Rather than changing the drainage of the site, you may be able to landscape with plants that tolerate occasional wet feet. Siberian iris (Iris), redtwig dogwood (Cornus), maiden grass (Miscanthus), and moneywort (Lysimachia) are a few examples of plants that may be suited to periodic wet cycles but which also thrive during drier times.
A well-qualified professional landscape designer or architect will save you money by providing detailed plans you can follow on your own when time and money allow. Ask for references from anyone you consult, and talk to more than one professional before hiring anyone.