Upon your arrival, the Israeli authorities are responsible for issuing a visa. The Palestinian Authority is not entitled to do so, as the borders of Palestine are controlled by Israel under its military occupation of the West Bank and the Gaza Strip.
If you come from an exempted country (e.g. USA, EU countries, etc.), a visa / stay permit (see picture below) is given to you at Ben Gurion Airport in Tel Aviv or at the King Hussein Bridge border crossing. This permit allows you to stay and travel in Israel and Palestine for up to 90 days.
You can check whether your country is included in the visa exemption agreement on the following website:
http://mfa.gov.il/MFA/ConsularServices/Documents/VisaRequirements-Tourists.pdf
Should your country not have an exemption agreement with Israel in place, you need to obtain your visa from the Israeli embassy/consulate in your home country before your visit.