The bottom of my garden is similar to what you describe. Constantly wet throughout the winter (maybe even a small lake) and very wet through a wet spring and summer as last year.
The answer is to dig a 2 foot deep trench and fill it with whatever rubbish you can find, eg. bricks, gravel, stones, etc. to form a sump.This can take 2-3 years before you notice any improvement in drainage - sorry but there is no fast solution.
However, to make the area acceptable, grow the ornamental grasses which enjoy having their `feet` in water - Miscanthus Sinensis, the Chinese Ornamental Grass which comes in many very attractive forms. There is the Zebra Grass (Miscanthus Zebrinus) - 6 foot green leaves with interesting Zebra type bands along the leaves, Miscanthus Variagata, beautiful long green leaves with long yellow edges to the leaves - grows to 6 foot. Go to your local nursery and buy whatever 2-3 foot plants which enjoy wet conditions - there are many and they will help to soak up the water.
All these plants are common and can be found without difficulty.