The West Bank is an area in Palestine. Most of the area is de facto governed by the state of Israel, including all borders. This means you will have to get in through Israeli borders such as the 3 crossings with Jordan or at Ben Gurion. Stamps of Israeli "enemy countries" such as Syria can lead to an interrogation. If you have the chance it's better to acquire a new passport before leaving to the area. Also, when entering Israel it's actually better to lie about your planned visiting of Palestinian areas. Border control doesn't like this.
When moving around within the West Bank it's very wise to always keep your passport on you. There are many checkpoints. The easiest way to get around is probably on a bicycle as you are considered a "vehicle" at the checkpoints and you can easily pass.