I hate to be the harbringer of doom
but if your field's very wet the amount of willow you'd need to plant to dry it up would do away with valuable space.
What type of soil do you have ? If it's a heavy clay and it's holding water you could try ploughing it and adding LOTS of 'organic matter' to allow it to drain more freely. But if it's already good soil and just wet, the ONLY way to get it dry is as SFS says - lay in drains. Look to where your closest (downhill) run off point is - whether it's a pond, river, reed bed, soakaway or road ditch there's bound to be SOMETHING you can use (it might just be further away) then dig the trenches and lay in the pipes.
What borders your top field ? Could it be that someone else is draining their fields onto your land ? Or a large area of dense forrest ? That can sometimes make the surrounding ground wet. It could even be that there's a burst pipe somewhere below ground in the field ? The fact that it's the highest field that's the wettest would suggest to me that something's amiss - it might be worth having a check at old plans for pipes etc and asking neighbours if they have problems. There might be an easier fix than having to lay in the drains (but I'd prepare yourself for that job if you really want the land dry and useable
)
Good luck, Karen x