Step 1: Materials
I've found this fabric to work well for the body of the costume. It's soft, breathable, and light enough to move around in but with enough weight to hold the package together. The downside to curly fleece is it can shed quite a bit when it's fresh, so it gets rather messy. However, a good thing about this is that the fur on the fabric was so long that it easily hid the many safety pins I used. Another good option is something called Flurr (fleece + fur). You want about about 2.5-3x whatever your height is.
1-1.5 yds of Black Chiffon/Mesh
This is the mesh-like material that will form the mouth. It is important that the material be see-through, since this will be your window to the outside world. The mouth will probably consist of 2-6 layers of this material, depending on the specific fabric you have. The most important part is that if you hold it up to your face, you can see relatively clearly through to the other side (usually there is a light source outside of your costume), but no one can see into your costume through the mouth (no light source within your costume).
Contour Shaped Sponge
You can pick this up at your local Home Depot for a few dollars. A good half-oval shape is what you want. The dimensions I found were 7.5"x3.5"x2.5", and I eventually cut in half length-wise however. This will form the lip.
Styrofoam Spheres (x2)
For the eyeballs. 4" in diameter will do, or 5" if you want to go bigger.
This will be essential to keeping the costume on your head. Pick out something that is light, nothing too thick. You don't want to start sweating too much while wearing the costume. It should have enough structure to it though stay firm and not flop around.
This should match the color of your costume. Thin pipe cleaners work well, you just need to buy enough of them to twist around to make a solid and flexible pair of antenna. Some glittery pipe-cleaner is also helpful in complimenting the solid colors.
Hot glue gun
Needle and thread (or staples)
Safety pins (various sizes)
A friend (very helpful to have someone to wear the costume as it is being created)