This is a glimpse of the hut i made for my chins.
Its about 21 inches long, 8 inch high, and roughly 16 inches wide. (Designed to fit a FN shelf) All made with only a drill, hammer and a razor knife. (plus cutting the wood if you need to)
Using a system of dowels you can put it together without the need for screws or nails or high end glue. While still keeping it quite simple.
Lets see if I can explain this and make sense.
You would need your safe wood and safe wood dowels. (mine were poplar).
And i would recommend 1/2 inch thick wood. While you can do it with thinner pieces, it might not be as strong, and it will definitely be a bit harder to work with. And the dowels slightly smaller then you main wood. I used 1/4 inch i believe.
Assuming your making a rectangle shape hut, take two pieces and place them perpendicular to each other. (Like an L to make a corner)
Use a drill to drill a 1 inch hole through the end into both pieces. (As if you were coming up from the bottom of the L into the long piece.) You can make them longer if you wish. You want to make it as close to the middle of the piece (horizontally) as possible. You don't want the hole ripping through the side of the wood.
Cut off a 1inch piece of dowel. To help more, take a razor blade and make a slight cut from top to bottom (long ways.) This will help remove air in the next step.
Put the dowel in the hole. You might need something like a hammer to knock it in all the way. Just be gentle. You don't want to break it. Now when you put a dowel into that whole the air has no way to escape. Thats where that cut you made on it comes in handy. The air can use that to escape. If you want some extra hold, you can use a dab of the safe kind of Elmer's glue in the whole before placing the dowel.
Once the dowel is in, you basically have the gist of the whole thing. Do that for each connection/corner of the hut, and the same for the roof. The amount of dowel per side is completely up to the maker. The larger it is, the more likely it is you'll need to use more. But i would recommend at least 3 dowel per connection/corner. One hole at the top, one at the bottom, and one in the middle. That should give it a secure hold when your done.
Just make sure when you dowel the roof, that you don't cut through the top corner dowel.
Thats how i made my two huts anyway. And i hope that made some sense. The only reason I mention all that is because i would imagine the shipping on an large hut fully put together would be a bit high. Plus you get the joy of saying you did it yourself.
Honestly for me, the hardest part was simply finding the right size wood to use.
Edit: You will need to cut a door for them to enter when your done.