But, when I was a little kid, if we made something with paper mache, we used a balloon and maybe some toilet paper rolls to make the armature, no matter what we were sculpting. But it doesn't have to be that way! Especially when you're a grown up and you want to make something a bit more detailed... or at least less balloon shaped.
Step 1: Making Your Armature (without balloons). Draw or print your shape(s) onto cardboard, foam core, or card stock. For more complex shapes, like a bird for instance, cut out separate pieces for each of the wings, the tail, and the body. For my project, I'm making a marionette head, so I only need one piece. I chose the side perspective because I think it's harder to get "right" than the front perspective.
Step 2: Using aluminum foil, start "bulking up" your shape to make it 3D. Hold the foil in place with tape. Normally, one would use masking tape, but all I had on hand this time was scotch tape. It still worked, but not as well. This is the part that is most awkward for me as a 2D artist. Thinking in 3D is a trip. Just keep bulking and shaping until you have a shape that is somewhat close to what you're hoping for. If your project was very big, you might use crumpled paper instead of foil.
Step 3: Using strips and bits of paper, create a layer of paper mache over your foil and cardboard armature to solidify your shape. It's certainly possible to buy paper mache glue, but it's much cheaper to simply put a handful of flour in a bowl and add enough warm water to give it the consistency of melted ice cream (add a dash of salt if you live in a humid climate). Or, alternatively, you can use white glue watered down to about the consistency of chocolate milk (ahh, dairy analogies). Allow to dry either in an oven set to 200 degrees Fahrenheit, or, if you're patient, allow to dry over night between layers.
Step 4: To get more subtle shapes and smoother lines, use toilet paper dipped in paper mache glue. With toilet paper, I can really start bringing out the shape of the cheeks and eyes, and also add some bulk here and there to get my face more symmetrical. If you want a smoother surface, you might try paper mache clay. The nice lady/amazing artist of Ultimate Paper Mache has a recipe and a lot of great tutorials.
Step 5: Paint and varnish! Paper mache normally needs at least two coats to cover the text from all that recycled paper you've used. And, varnish adds a bit of durability to something otherwise made of paper and flour.