First, get yourself a super cheap, clear plastic hair comb. This is going to be the base on which you attach the veil and decoration.
Go to the fabric section of the store and buy some tulle. You want to buy a bit more than however long you want the veil to be. It'll come as a square, but when you get home you can trim it into kind of a petal shape. Gathering it as you go along, hot glue it to the flat part of the plastic comb.
Then, cover that whole part with a piece of white satin ribbon (or, you know, whatever color you want, if for example Fuschia is your thing). Attach this with hot glue so you know it'll stick really well. You're going to glue your decoration on top of this part so if it's not absolutely perfect or straight or bump-free, that's ok.
I was going for a 50's inspired birdcage veil with pearls so I hit up the beadmaking section of the store and discovered that you could buy a little strand of authentic freshwater pearls for about $4. I cut these off the string when I got home, and then hot glued them to the ribbon in a cluster that was visually appealing, filling in any holes or bare-looking areas with some smaller fake pearls that I had lying around.
Boom: birdcage wedding veil for $15. Which, if you ask me, is the right price for something I'm going to wear for a half hour.
Detail of the pearls.