Cultivating the ground should improve the drainage.

Plants for wet ground

Wet areas can be exploited by growing plants which tolerate or need wet roots, eg shrubby willows, hostas, primulas, guelder rose, native daffodil, dogwoods.

Drains?

If water still stands for a long while after rain, think about installing drains. But remember that bare ground which appears to be badly drained is improved greatly once planted - plants use all the moisture.

Drains have to take the water somewhere - either to a large hole filled with stones (a sump) or to another drainage system (check with the relevant authority).

Paving reduces drainage area

Remember when you are designing your garden that paved surfaces create a double whammy - reducing the area of soil for dispersing water and producing run-off.