This is a (mostly) complete, working enclosure that has been able to maintain heat/humidity the same as a 55 gallon tank (1/4 the size of this), with the same lights/etc. I started with a Sears rolling cart (used, they used it to hold pillows/sheet bundles/etc.) for $40 from a store that was going under. I really liked this because the frame could be strengthened and everything could be tied/secured to the wire frame without having to use too much adhesive.
Step 1: Tighten Up the Frame and Measure Out the Insulation/liner.
The frame will need to be adjusted - retail staff use these carts, but they don't really maintain them. There's a lot of little bits that need attention/adjustment on the corners and connections. Take your time and make sure they're all tight and the frame is straight.
After that, measure out the foam insulation sheets and the liner (I used a shower stall liner, flexible and mold/mildew resistant, so it can be bent as the inside wall without having to use sealant to seal the corners). I did not glue the sheets or the liner in place - instead, I used Zip ties and garden spikes (4 feet tall) as the corner mounts - zip tie the spikes to the wire frame, and they'll hold the liner in place easily.
Step 2: Build Your Roof/outer Walls.
So here you can be as creative as you want - I am using thin particle board sheets with a smooth veneer on the outside, zip tied to the frame the same way as the inner liner. I also made a simple box frame lid (1x2s as the frame, stuffed with more foam insulation, then particle board top and bottom). I did make it with thicker particle board to make it heavier so the iguana can't push it open to get out. You can see on the last image here the foam inside the lid. I also did not add the outer wood to the back wall since it wasn't needed and saved a few bucks.
Step 3: How to Make a Clear Window Without Having to Drill Through Acrylic!
The simple answer is, don't use acrylic sheets. I found out you can order this plastic sheeting (for kitchen tables/desks) on amazon at just about any size you need, so I measured, ordered and didn't even have to trim it to fit! The sheet is secured to the door/window by bootlaces punched through the edge.
Step 4: Waterproofing Your Interior
The advantage of the shower liner is you don't have to waterproof TOO much. I went with a PVC underlayment used for tile that can be cut to a specific size that was placed to seal the bottom of the enclosure, using a clear (well, dries clear) sealant to hold it in place, as well as the sheet of insulating foam underneath the pvc on the lower front wall, with a couple zip ties on the front frame for support as well.
Step 5: Cut Some Holes!
This was just a quick cut with a jig saw (with a drilled hole to start it off) at 9 inches, slightly larger than the heat lamps I'm using. To keep the lizard safe, I screw in a couple splash lids from pots and pans (since they have a metal rim around the wire mesh for strength) to the bottom so there's a screen on each.
Step 6: Build Your Inner Climbing Tree
I built it simple, with just a couple layers out of poplar dowels, zip ties and some burlap meshing. The burlap is folded on itself in 3 layers first, then bound to the poplar as a climbing net in the corner and as a hammock on top (angled, so the iguana can adjust how close she is to the heat lamps to adjust her internal temp on her own).
Food is on the step in the back, and the water bucket is just a thick rubbermaid tub from Home Depot (lifetime warranty!). I also added a small 2-10 gallon fish tank water heater so the water won't get too cold during the winter here in Washington.
Step 7: Keep an Eye on Your Iguana!
If she spends too much time too close to the heat lamp, it means the tank isn't keeping warm enough - switch to a larger wattage lamp or think about adding another in the lid. I also added two thermometers and a barometer to keep track of heat and humidity throughout the tank.