Bunnies/Rabbits - Ideas needed on how to house them comfortably and easily

[RealLifeMama]

DD has two bunnies.
The people that gave them to us gave us a wooden hutch as well. It has some chicken-wire-like-but-not-chicken-wire stuff on the bottom. We are keeping them on the porch.
Right now, we are lining the hutch with hay.
It is a mess.
I am not really sure how to even clean their cage. We were told just to put in a few inches of hay, but not only is it getting expensive, it is just really hard to clean the old hay out and put new in, keep it dry, etc.
They don't seem to discriminate where they use the bathroom. Is that typical?

Last week, we set up some cinderblocks, put down some big cardboard sheets, then put the hutch overtop, then the hay in the hutch. I can just roll up the cardboard that is soiled and replace it, but that is not a permanent solution.

Help!