Watch the news and check the situation before you go. It isn't a good idea to visit if fighting between Hamas and Fatah, or between the Palestinians and Israelis, happens to be intense at the given time. However, violence in the West Bank tends to be very localized. Violence in Nablus, for instance, shouldn't necessarily hinder travel to Ramallah. Still, use discretion.
While non-Israeli Jews are generally left alone and sometimes even openly welcome, symbols associated with the State of Israel or Zionism, such as the Star of David, are best left at home. Espousing blantly pro-Israeli views will highly offend many ordinary Palestinians and is not recomended.
talk
The main languages in the West Bank are Arabic and Hebrew, although English and French are also understood. Many Palestinians understand Hebrew, due to business and governmental contacts over the last 40+ years. But avoid speaking Hebrew in Palestinian cities and Arabic in Jewish settlements, as it may arouse suspicion. Russian is also common among students who have gone to university in Russia or Eastern Europe. A few Israeli settlements contain Hasidic Jews who speak Yiddish.
respect
The West Bank is less 'religious' than most Arab nations, so women travelers don't need to be completely covered. But it is still a good idea to dress fairly conservatively. With Palestinians, one should not insult with western mocking jibes at Islam or Arab heroes. Again, like Israel, one should not talk disdainfully about Torah, Holocaust, or Jewish history insofar as getting dirty looks from confident new settlers.
Be very wary of bringing up politics and the Israel-Palestine conflict, for obvious reasons.