I also endorse ANR. Let me also recommend Scott Sullivan's Virtual LM and the always venerable Chariots for Apollo. But let me also give an answer off the top of my head, from accumulated knowledge.
I also can't endorse Jason's point enough. All of them. If you saw a lunar module without its clothes on (and there are plenty of pictures from various sources) you'll see a surprisingly robust aluminum skin-and-stringer construction. That provides the structural strength -- quite a lot of it. The thermal and other requirements then get to be satisfied by other materials that don't also have to contribute to the structure. This is what you get to do when your spacecraft doesn't need to withstand fluid flow against and around its outer skin. Contrary to lay misconceptions, films, film blankets, and coatings work best for this. The goal is to save weight. I'm surprised that people are surprised by film blankets. Quite a lot of spacecraft at the time and subsequently have outer skins made of blanket or various metalized films. The LM is not out of the ordinary.
Last part first. People wonder about the tape. Yes, it's tape. But it's not household masking tape or duct tape or anything so pedestrian. Laymen are always flabbergasted to learn that industrial versions of tape exist. The most common is "speed tape," thin aluminum sheeting backed with industrial-strength pressure-sensitive adhesive. What you see on the LM is likely Mylar or Kapton tape. That too has an industrial-strength pressure-sensitive adhesive. Adhesives that strong are not routinely sold to the general public because of how the general public generally behaves. Yes, it can stick ferociously to skin. Tape is used in high-end engineering for precisely the same reasons it's useful around the house. It's often the best way to fasten two things together. Seaming two sections of a blanket or thin sheeting isn't best done with a piercing fastener, as tearout would inevitable result. Tape spreads the load properly.
Attachment to the LM secondary frame, however, sometimes used properly protected piercing fasteners, usually to a standoff that kept the blanket the proper distance from the inner pressure vessel. This is nearly identical to the way insulation blankets are laid up on airliners. Not all of that is visible from the outside of the LM.
The various materials for the film blankets, e.g., aluminized Kapton, come on rolls. Manufacture is merely a matter of unrolling the materials onto a table to build up the layers (in a properly controlled environment, of course). Some blankets have layer-contact constraints, which means each layer has to be crinkled randomly so that it doesn't make full contact with its neighbors. As this was most effectively done by hand, the size of the resulting blanket stock was limited. This is why the outer skin had to be assembled in patchwork fashion. You gain nothing by trying to cut patterns in the material before lamination. It's just as effective -- and far easier -- to custom-cut the finished blanket and then join the patches with tape.
If you examine LM-2 closely, you'll see that its aft equipment bay covers are neatly screwed into the secondary structure via correctly-space overlapping eyelet holes and proper grommets. That's how you'd design it "properly." But you see LM-5's AEB covers just taped on. That's how I'd expect the design to turn out after several passes of design review with attention to manufacturability and weight savings.
The lunar environment is not "hostile" in all the ways the Earth's is and then some. It's just more hostile in some ways and more forgiving in others. When you have no air, and you have a piece of material whose only job is to keep the sun from shining on something -- not fend of spear-throwing aliens or giant squids -- then that material should be as gracile and light as possible. The lunar environment is more forgiving than Earth's in terms of physical weathering.
