There are no international airports in Palestine, so you can only enter overland through Israel. In general, Americans, Canadians and most Europeans do not need a visa in order to enter Palestine.
Please refer to Israel’s Tourist Visa Table to see if your country requires a visa to enter Israel. As a Palestinian visa does not exist—if you have an Israeli visa, you can visit the West Bank.
Upon your arrival at the Israeli Airport in Tel Aviv or Eilat, you will find a queue of people waiting to pass through security. If you are questioned about your trip, remain patient and calm and answer their questions.
Afterwards, you will be granted a tourist visa valid for 90 days that enables you to travel around Palestine and Israel. As Israel does not stamp passports, you will instead be given a paper slip, which you need to keep with you at all times when traveling throughout Israel or Palestine. You can read more about visas and traveling to Israel/Palestine here and here.