High susceptibility to bacterial infections and vulnerability to parasites are two of the many challenges faced by chameleon keepers. Proper air circulation greatly reduces both of these threats. For this reason experienced chameleon keepers prefer to use enclosures constructed mostly if not completely of screen. The ground dwelling  species are an exception and may be housed in terrariums.

Terminology

Click pic  to view a picture of the tool or supply.

Tape Measure pic
Box Cutter/Carpet Knife pic
Scissors
Spline Tool pic
Hammer pic
Standard Straight Slot Screwdriver pic
Drill pic
1/16th inch, 1/8th inch, and a #1 Philips head drill bit pic
Hack Saw and Miter Box pic

10 - 8 ft screen frames pic
8 packs of 4 corner braces pic
1 knob of choice (may substitute loop latch) pic
50 self tapping #8 3/4inch sheet metal screws pic
1 pair of 1 inch hinges pic
50 ft of .125 screen spline pic
Package of 8 nylon turn buttons pic
Package of 4 wire loop latches (used to pull door open) pic
16 ft X 2 ft screen
Masking tape

Measure and cut the screen frames.
For this design, you will need:

6 pcs 36", 5 pcs 26", 10 pcs 23^3/4", 2 pcs 23^1/2", 4 pcs 23^1/4", 4 pcs 16"

1 pcs 15", 2 pcs 8", 2 pcs 5^3/4"

Here's how these are used:

I used the Stanley Clamp Miter Box. It has convenient peg clamps to hold the piece you're cutting.
I marked the frames by scoring them with a screwdriver (top of image). Place the scored line in the center of the 90º cut guide on the miter box (bottom left inset). Clamp the frame piece in place and cut with the hack saw (bottom right inset). Remember to "measure twice and cut once."
 

Assemble the screen panels.

Each enclosure is a six sided box constructed of screen panels. Group the cut frame pieces into the 4 sections needed for each screen panel. This design calls for 8 panel frames; the top and bottom, right and left sides, the back, and three panels for the front of the enclosure. The three front panels are the door panel, a support panel and a lower swing panel to facilitate cleaning. Your panel measurements are:  two panels 25^1/4" X 24^3/4"for the top and bottom, two panels 25^1/4" X 37^1/2"for the right and left sides, one panel 25^1/2" X 37^1/2"for the back, one panel 9^1/2" X 25" for the swing panel, one panel 7^1/4" X 27^1/2"for the support panel, and one panel 17^1/2" X 27^1/2"for the door. 
 

Insert a screen frame corner into each end of two cut sections from one panel frame (bottom right inset). The screen frame corners are designed to be "Murphy Proof" meaning you can not put them on the wrong way. Now insert the adjacent frame piece from the same panel frame into the other side of the screen frame corner piece to form an L. Repeat this with the last piece of this panel frame. Connect the two "L's" together by sliding the open ends into the open end of the screen frame corner piece. This should form a square or rectangle depending on which panel frame you are assembling.
Repeat this until you have assembled all of the panel frames needed to construct your cage.
 

Assemble the panel frames and secure them together using the masking tape. See assembly diagram. The two sides fit against the back. The top and bottom will be inside of the back and two sides flush with the back. All three of the front panels are attached inside the sides, top and bottom. Check all corners and edges for a square and tight fit. If you need to make any adjustments, it is easier to do so before the screen is installed.
 

Pre-cut the screen to the size of the panel frames. If you are using a soft poly or fiber screen, you will need to allow a couple of inches over hang. If you are using an aluminum screen, cut it to fit with only 1/4 inch overhang all around. The poly/fiber screen is easier to work with, but panels made with it are not as strong and may not support plants or withstand the extreme heat of basking lamps. You may want to use a sheet of plastic (PVC) or aluminum screen for the bottom and aluminum screen for the top. Lay the screen over the frame Start at a corner and push the spline into the spine track. Use the spline tool to push the spline into the track all the way around the frame (top inset). Push the corners into the track using a screwdriver (center inset). When constructing the swing panel, insert the wire loop latch before pushing the spline into the track.

 

Assemble the enclosure temporarily using masking tape to hold the panels together, as done in step 3. Drill a 1/16th inch pilot hole approximately 3 inches from the edge and 1/4 inch from the top of the right side screen panel continuing through the top screen panel (top inset). Pre-drilling ensures that the holes lineup and that your screws do not "travel" across the frame piece. Screw a self tapping #8 3/4inch sheet metal screw into the pre-drilled hole taking care not to over tighten it. Repeat this process until you have 4 screws on the long panels and 3 screws on the shorter panels of the top, bottom, back and two sides. The front panels will be handled differently.
 

Final Assembly - front door, support panel, and swing panel.

Cut a 30 inch and 18 inch piece of screen frame for door stops. Measure and mark 5 inches and 12 inches from the top and 5 inches and 12 inches from the bottom of the support panel. Drill four 1/16th inch pilot holes on the marks as close to the outside edge as possible. Place the 30 inch piece of screen frame (door stop) on the back side of the support panel allowing as much as you can to overhang. Install a nylon turn button to the support panel and door stop in the top and bottom holes using the #8 3/4 inch screws. Screw two more #8 screws in the two middle holes. Secure the other door stop to the top inside (bottom right inset) using the same procedure. Drill four pilot holes in the left side and into the support panel and two holes in the top and into the support panel and secure it to the enclosure. Drill a 1/8 inch hole in the door panel in the middle of the left side and secure the knob (left inset). Drill 1/16th inch pilot holes and secure the hinges to the right side of the door about four inches from the top and bottom of the door panel. Measure 4 inches from the bottom on both sides and pre-drill. Screw the swing panel in place. Install a nylon turn button to each side of the swing panel about two inches from the bottom of the panel. 

Rinse or vacuum inside the enclosure. The drilling will leave metal shavings which need to be removed before use. Add your choice of plants, lights, and hydration equipment and your ready to move your cham in.