Who is responsible for the partition of Palestine? What governmental bodies or individual governmental actors were the driving force behind the action? If there were non-governmental actors that played a role in this I would like to know that too.
Most recently the borders were mandated by the United Nations after WWII. A two state solution was proposed and essentially forced on the Israelis and Palestinians. Since then there has been near constant fighting and the borders have moved as a result of successful military campaigns by Israel most notably the Six-Day War.
The area has been in a near constant state turmoil though for hundreds of years and truth is really a matter of perspective of what time frame and side you want to focus on.
TL;DR: Responsibility for the existence of "Israel, East Jeruaslem, the West Bank, and the Gaza Strip" instead of just "Palestine" or "Eretz Israel" can be attributed to: the British Mandatory authorities, the Zionist movement, local Arab populations, the leadership of the nascent Palestinian Arab movement, and the Jordanian and the Egyptian governments.
The region known historically to Europeans as Palestine was divided among a number of villayets or districts of the Ottoman empire until World War 1.
When Britain and France had defeated the Ottomans they divided up the spoils, and assigned a chunk of territory to British suzerainty as the British Mandate for Palestine. The British decided to support the Zionist movement among European Jews and, for a time, favoured Jewish immigration to Palestine and national claims.
British policy however was two-faced and as time passed their support was flagging and inconsistent. By the immediate post-WW2 period the British were exhausted by years of total war and multiple colonial crises. The Mandate was due to expire in 1948 and there was no remotely graceful British "exit strategy." They punted the question to the United Nations General Assembly, which issued a non-binding recommendation for partition into Jewish and Arab states.
The majority leadership of the Zionist movement accepted the partition plan, although right-wing Revisionist Zionists openly demanded more territory, and it is probably fair to say that Ben Gurion et al. anticipated having to "normalize" the new state's borders by military means. Almost all Arabs rejected the partition. Aside from flat opposition to the establishment of any Jewish state in Palestine, they also objected to the proposed borders, which would have entailed a very large population of Arabs living as minority citizens within the new Jewish state.
In the end the impending British exit and the contemplated partition led to a civil war between Jewish and Arab militias within Palestine (mostly local Palestinian Arab militias, with some involvement of volunteers from Jordan, Syria, etc.) The Zionist forces rapidly gained the upper hand and consolidated their territory. Atrocities and expulsions magnified by rumour and confusion led to a mass exodus of Arabs from Jewish-held zones.
After the formal termination of the Mandate the civil war became an international war with the intervention of multiple Arab armies in May 1948, almost simultaneous with the Jewish community of Palestine's declaration of independence as the State of Israel. The situation was initially very difficult for Israel as a powerful Egyptian offensive moved up the coast from Gaza and a large Jordanian army besieged Jerusalem. However their better co-ordination allowed them to stabilize the situation, and diplomatic support gained them a series of cease-fires and an arms embargo which in practice they could circumvent while the Arab forces could not.
By wars end the Egyptian forces has been almost entirely expelled, except for a narrow strip of territory around Gaza City and Rafah which became known as the Gaza Strip. The Jordanians fared somewhat better, holding the Jordan Valley, the Old City of Jerusalem and a broad re-entrant around the western approaches thereto, and most of the rough hilly territory in between. This became known as the West Bank (including East Jerusalem, which is also sometimes discussed as a separate territory still.)
Later, in 1967, Israel captured these territories from Egypt and Jordan. These occupied territories have been de facto integrated into Israel proper in many ways, and an expanded Israeli-defined East Jerusalem has been de jure annexed, although pretty much every country in the world defines this as an illegal and unrecognized claim.
So, roughly speaking:
"Palestine" is not an entirely well-defined area, and all the myriad political entities that have existed on its territory have been sliced, diced, and partitioned every which way since time immemorial, just like most places on Earth.
The current division between pre- and post-1967 Israeli-controlled territories -- I and most of the world would prefer to say, between Israel and the occupied Palestinian territories -- resulted from the 1948 international war between Israel and the Arab states. This war resulted from the 1947-48 civil war between Zionist and Arab militias, which resulted from the mismanagement of the British Mandatory authorities, the territorial ambitions of the Zionist movement, the intransigence of local Arab populations in the face of Jewish settlement, and the incompetence and anti-Semitism of the men the British had promoted as Palestinian Arab leaders. So all of the above bear responsibility.