Adabot has six main pieces. The head, torso, two arms and legs are separated for articulation. You can glue the parts together or use paper fasteners as hinges. You'll need to punch holes into the material. Use mounting tack for temporally holding them together. Using snaps could be a great way to make hinges as they can be easily detached.
I suggest using an extra strength glue stick to secure the layers together. The one I'm using is from Elmer's, called "Extra Strength", it goes on purple and dries clear. Just be careful with the thinner features. You’ll want to make sure your parts are in right orientation when applying the glue. Line them up first and check to see if they’re mirroring. Most of these shapes can be lined up nicely by squaring up the edges. If they’re slightly off, you can adjust them by carefully sliding the layers to line them up.
Use a good amount of glue stick, especially near the edges. We don’t want them to lift, so you’ll want to cover as much as possible. For very small details like Adabot’s ear cups, I use a pair of tweezers to wipe it on the tip of the glue stick. This way we don’t cover the unwanted areas with lots of glue.