Regan, the character played by Linda Blair in the movie the exorcist, underwent a grueling exorcism that left her exhausted, malnourished, dirty and battered.
Keeping that in mind, you should portray this in your hair, facial features and clothing. For a homemade costume, you'll need the following:
Medium to dark, brown hair or a wig is essential. If your hair is not brown and you can't find a wig, use fanciful temporary hair color that will wash off easily whenever you're ready. You can find it at Walgreen's or discount stores such as Wal-mart. (Do not use this if you're going to be in the rain, it can wash off onto your clothing). Use hair gel to create stringy bangs and strands of hair. The gel will also darken your hair a bit if it is lighter brown. Your goal is to make your hair appear brown, dirty and un-kept.
Some stores sell makeup kits that come in handy, especially for the hard-to-find green goo. If you don't have a makeup kit, try using what you have at home. Start with a clean, dry face. Prepare your face with white makeup. If it feels greasy, you can set it with loose, translucent powder or white powder.
Create dark shadows all around the eyes, with a charcoal or black eyeliner pencil. Rub and blend it in so it looks smudged. Accentuate creases in the face and lips by drawing them in and blending, particularly from the nose to the mouth, which will help re-create Linda Blair's puffy cheeks. Follow your own natural creases when making an appalling expression.
Make realistic fingernail slashes with a recipe for fake wounds or draw them on with the eyeliner pencil and red lip liner. Add homemade fake blood or that from a kit sparingly to the slashes and to your clothing if desired.
Visit your local thrift shop or goodwill for a frumpy, light blue housecoat or robe. One with buttons and not a zipper would look more authentic. Depending on where you'll be walking, you can choose to wear slippers or plain brown shoes.
The creepy, bloodshot eyes are key, but not completely necessary. Besides wearing contact lenses, not much can be done here. You can try lining the rims of your eyes with reddish or pinkish liner. Do a trial-run to test for irritation.
Look for fake, stained teeth which are depicted in many scenes in the movie. When I last checked, Wal-mart had some that were just perfect, in the party favors & Halloween section. You'd end up buying a few pairs but they were very cheap. I'm sure you can find a set in other stores as well. They sell quickly so if you find some, get them now.