Hoodoo is a magical practice and, although it shares many ideas with Voodoo/Vodou (and other Pagan practices) and even a few things in Christianity, it actually has nothing to do with any particular religion.
No, you do not have to believe in God in order to practice Hoodoo. There are many different types of people who practice. I have known of Christians, Mambos (Voodoo Priestesses), and Pagans (myself being one of them) who practice Hoodoo, all with equal results.
There are no real religious beliefs in Hoodoo (at least no dogma so to speak). It focuses purely on the practice of folk magic. It's used in matters of luck, love, gambling, weath, cleansing, protection, and hexing. Since there are no real religious beliefs attached to it, the ethical application of it is up to the practictioner. For example, Wiccans practicing Hoodoo would not do anything to imposing on another's free will since they believe in the Threefold Law (everything you do comes back to you three times over). On the otherhand, someone who did not have a belief in consequences would have no problem doing it. It's really up to you and what you decide to believe.
Since there is no hierarchy in Hoodoo finding a teacher can be hard. I do suggest you try to find one though! Cat Yronwode, the owner of the Lucky Mojo Curio company, is quite knowledgeable and offers a correspondence course for a fee. If that isn't the route you want to take, you could visit your local "New Age" or "Witchy" shop (if there is one near you) to possibly find a teacher. And if you're still having problems after that, you might want to search Amazon for books. "Sticks, Stones, Roots, and Bones" by Stephanie Rose Bird is a particularly good one, and "Hoodoo In Theory & Practice" by Cat Yronwode is an incredible resource as well.
There is a lot to practicing Hoodoo, and I'm afraid I can only cover a little here, probably to the point it doesn't give you a good idea about it just yet, but I do hope this helps.