How do you screw stuff into the walls?

I have had some success using the spiral sheet rock anchors in areas where no stud or metal framing was available.

We have put screws in our walls without searching for studs but we also don't hang anything heavy. We use small #6 wood screws. After 2 years everything is still attached.

I have a piece of wall that I removed in the door to install a window. The walls are NOT hollow like what you expect in your house when you put a dry wall anchor thru the drywall. There is a condensed foam insulation between the inside and outside wall(s). I want to try different anchors and see how they expand in that condensed foam. I can use that piece I cut from the door. There is about an inch and a half between inside and out side walls. You have to be careful when drilling from either side not to go thru the other side. You just want to pierce the interior wall. Same with hanging something on the outside, I have solar security lights motion lights I mounted. I use an old trick, when drilling anchor holes. I wrap electrical tape around the bit about a half inch from the tip, that stops the bit from going in more than about a half an inch. I'm using the bit that comes with the anchor set, I believe it is a 1/4 bit for a number 8 anchor. I have not used the anchors that Stephen suggests but I will test them now to see how they anchor in the condensed foam. I have used Crown Bolt anchors for many applications. Very secure. I don't use the walls in the RPod to hold anything of weight. Light bearing shelves are ok, but if I want to hang clothes for an example I use a closet rod above the window shade boxes so everything is load bearing. Then I attach the shelves to the closet rod so there is an assist to the shelf, if that makes sense. You do need a stud locator that warns of metal studs, if you do or don't want to use the existing studs. I haven't found any application where I could use the existing studs, different for everybody.

Given that the walls are 1-1/2" thick, a 1" anchor will definitely NOT go through the outside. Don't make the mistake of getting the Short Hollow Wall Drive Anchors (with the pointed end). They will definitely go through the outside wall (speaking from experience ). Just be careful to only drill through the inside wall as described by Mike Carter. His idea to put a piece of tape on the drill bit is a good one.

Don't bother trying the "Toggler" anchors that look like wings. The foam makes it almost impossible to push the wings into position, which means that they can't perform adequately.

Again, thanks for the correction. I was assuming that the door and walls were the same thickness. Still, a 1-5/16" wall should be in no danger from a 1" fastener.