This is a pretty bad shot of its construction, but there's my very first cage on the far right, and new ones on the left and in the middle. I used 1 1/2"x1 1/2" spruce for the frame, some flat board to go in between cages, "L" brackets for hodling the whole thing together, and some press board for the bottom screws etc. each cage cost about 50$. I would strongly reccomend NOT using L brackets, just use screws and try not to split the wood. The something like 48 L brackets I needed cost almost as much as everything else needed for each cage...about 20$ per cage just for the brackets...
Use 1/2"x1" spruce for the door and get some small hinges to go along with it.
Be sure to measure all the lumber you need, and add a few feet to make up for mistakes, you will need it if you don't make plans, and even then, mistakes happen.
Be sure to paint everything and put silicone (preferably aquarium grade to ensure it being non-toxic) around the bottom seams to prevent leaks from puddles after misting and dripping. Use whatever kind of screen you fancy and staple it into the frame, with a reccomended 3/4" staple. I used 1/4" and it works fine, but for thicker screen a larger staple is needed.
good luck building...I just went by ear on them and didn't really make plans, if you have any creative skills at all this isn't a problem, it's just a bit time consuming. I think it was my method of L brackets that took the most time.