Consider using the search button, which sits along the bottom of the Banner across the top of page. There has been several excellent Posts address this question.
What building skills do you have? What knowledge do you have in material selection? Have you started with your local Zoning to see if you can even build such a structure and if you can, what are the Building requirements? What access-ability do you have to the needed materials, contractors and suppliers? Lots to think about!
To build a good Aviary for outside use requires much more than you are likely thinking of at this point. Electric Source (outlet(s) near the Aviary. Electric Lighting (yes, you will want it and its a real pain to add it later). Water source(s) near the Aviary. Proper drainage of waste as part of the design. Concrete base to prevent animals digging into the Aviary. Side walk or stone walkway to the Aviary (when the grass turns to mud, this will become clear).
Also, what about a double entry, i.e. it should require an outer door and a safe space with both the outer and inner doors closed prior to entering the Aviary. Have you considered locks of the doors to keep the Aviary as a safe place when (Not If) you leave the home with the MAC still in the Aviary.
Doing this Right, the first time, requires a ton of planning and regardless of whether it is a DIY or with a Contractor its going to cost real money!
There are many good quality aviaries out there, but they can be into the thousands of dollars. Making it yourself would be a fun project, but expect it to cost several hundred dollars in materials, as well as spending many hours building and setting it all up. 
