The Palestinian Authority areas are a hitchhiking paradise. It's extremely safe and easy. In general you'll be able to get a ride from the first five cars that pass by. People are really helpful and hospitable, sometimes too much. You'll end up with loads of dinner-invites, telephone numbers, cd's of your favourite arabic music etc.
A woman hitchhiking by herself is seen as weird, but therefore people feel it's their obligation to make sure a woman is safe. They might insist paying for public transport for you to make sure that you arrive to your destination without any problems. Alternatively, there is a prejudice that western women, and women who are wearing their hair uncovered, are sexually promiscuous, which some men might translate to 'will obviously have sex with me.' You might want to help yourself look more desexualised by wearing a headscarf, or only getting into cars with women already in, but there are a lot more men on the road. Be aware that the roads can be quite empty and desolate between towns, and you might want to try and hitch not in the middle of no where for safety. Although the quiet places are beautiful!
Be aware that many of children (and probably adults) in Palestine suffer from Post Traumatic Stress Disorder. Younger people will normally be amazingly friendly and loving, but also may show strange symptoms of trauma in their lives. Be watchful, but also understanding.
A quick note on dress in general. Most Palestinians are Muslim, and you may, especially if you're perceived to be a woman, want to dress very modestly to avoid extra hassle. In general it's nice to feel that you can fit in to a certain degree, and so covering past over your knees, and your shoulders, will probably allow you less stares. Obviously this also helps for the heat! The same might go for tattoos and piercings.
A lot of cars may expect you to pay towards gas money, which is pretty expensive in the Palestinian Authority. This is one hitchers experience of hitchhiking in the West Bank anyhow. If you go by the drivers recommended 'donation' you may end up paying more (or, perhaps a lot less) than you would by getting a taxi. You could probably make it clear that you have no money and they can decide whether or not to take you.
English is not so common. Be aware of what language you begin speaking to the driver in, as a lot may be assumed about your politics or origins from a simple hello in Arabic or Hebrew. It's recommended to get to grips with some basic Arabic, and maybe less importantly, some Hebrew, although some IDF (Israel defence forces, who work on the check points) may speak some English.
Generally, hitchhiking in the West Bank can be done along side any road, you don't really have to find a strategic location. However, hitch-hiking around checkpoints might create a little confusion for Israeli soldiers. They might think you're Israeli and they will try to prevent you from entering Palestinian cars. When they realize you're not Israeli it's fine. They could try to warn you for "the dangers" of hitch-hiking with Palestinians. Similarly, some Western looking hitchers might be assumed to be Israeli settlers which some Palestinians may view unfavorably. Dreadlocks and colourful "hippy" (for want of a better word) clothes are also associated with Israeli travellers.
In the West Bank you have to be a little aware of where you want to go and who's driving. If you get a ride with an Israeli settler, they will not be too happy to hear that you want to go to a Palestinian city. But if you like the discussion, go for it.
Israeli-issued numberplates are yellow, Palestinian Authority-issued numberplates are white-green. However a lot of Palestinians also drive yellow numberplate cars.