Our goat housing is on the ground and I have not ever, yet, had a problem of areas that are constantly wet. The ground is not level in that it has a slight slope to the southwest. I use pallets inside the housing so the goats are not on the dirt if they don't want to be on the dirt. I do not put hay on the pallets inside the housing. The goats don't seem to want it and it makes it easier to throw down some lime to keep the dirt "sweet". My goats have absolutely no problem sleeping on the dirt, sleeping on the spent hay, sleeping in the feeder, under the feeder, on top of their shelters or in their shelters.
When we get the winter and spring rains their area does get muddy and the little darlings don't like walking in the mud so I have a path of pallets through their area so they, and I can get from one side to the other without dipping our precious toes in the mud. During the remainder of the year I rake around the pallets to gather up spent hay and poop.
I'm not sure how to address your question on drainage... it depends on how your land flows. Do you have a specific problem in mind? Maybe a picture or two would help with advise. Oh, and please put a general location in your information. It is very, very helpful to have an idea where someone is as often advise is location specific; as in what works in North Central Texas may not work in MN.