Avoid using mesh or other wire type sheets that are galvanized (zinc), because zinc is poisonous to birds. Its difficult to find acceptable material that is not really expensive. And if you use wood for the frame, it has to be non-treated and of course your birds may chew the heck out of it.
Here is an all aluminum one on Amazon. You will likely spend this much if you try to do it yourself with the proper materials.
I actually bought an aluminum one from the company listed above off ebay. Don't do it, it is not for parrots. Its more like for chickens or finches or something. The aluminum frame is fine, good quality. However, the aluminum mesh is a kind of expanded metal type. Its is sharp and not suitable for a parrot. Luckily we returned it. I'm carpenter and thought I could get away without building something too bad haha. Construction started this week. Mine will be as said above untreated 2x4 and stainless steel hardware cloth. Hope this helps.