The simple version is worked just like a basket. In case you want to make a cozy nest yourself there are plenty free patterns online that can be used. If you need help with finding one send me a message and I will try to help :)
For the more complicated version I used a flexible plastic rod that I saved from a window cover. I bent the rod in a circle and used it to created an entrance to the nest to create a cozy effect. I crocheted around the rod and because the thread was so bulky it maintained shape and did not collapsed. If you want to make something similar I do not have a written tutorial but I did make some photos to illustrate what I did. And in case of getting stuck send me a message I will do my best to help you.