How did the Jews occupy the land of Palestine from the Arab Muslims?

Answer 1
By the 100% help from England, and later by USA.
and it was started when Arthur James Balfour who made the Balfour Declaration on the 2nd of November 1917 which was a formal statement of policy by the British government stating that :

"His Majesty's government view with favour the establishment in Palestine of a national home of Jewish people, and will use their best endeavours to facilitate the achievement of this object, it being clearly understood that nothing shall be done which may prejudice the civil and religious rights of existing non-Jewish communities in Palestine, or the rights and political status enjoyed by Jews in any other country."

and England agreed on that and started to make this Declaration real.

So the land was occupied and taken from the Palestinian people, most of whom were forced to leave their houses, lands and their lives, because of both Israel and England. They now live in camps in Lebanon, Syria, Egypt, and Jordan and they are not allowed even to visit Palestine.

Answer 2

Issues of Moving Parts
This question has a number of moving parts, which makes it difficult to answer. For example, if I ask "Is the sky blue?" there are two things for which I need a definition. Thankfully the definitions for "sky" and "blue" are almost universally agreed upon, making the question answerable. The terms "occupy from" or "steal", and "Palestinian land" are far more nebulous.

As for theft, theft requires proper ownership. The first view of ownership is the literal definition of possessing something. Therefore whatever persons, companies, organizations, or governments own something with proper title as viewed by recognized governments are those who have "ownership". (This is like any typical sale.) The second definition is the perceived Color of Right of Title, which is to say that a certain person, organization, or government should have proper title but does not have it on account of an illegal activity (such as theft). (This case would come for example if A owned a book and B stole it. While B has physical possession of the book, A still retains ownership since stealing, the act of transfer and acquisition, is illegal.) Understandably, most Israelis claim that no illegal act took place and therefore title properly belongs to them. Palestinians and their sympathizers often (but not always) argue that their land was stolen and therefore, they retain proper ownership.

This difference in opinion is very important to acknowledge. If Israel is correct in its assertion that it came into existence as an independent State with rights to the lands of that state, then there is no theft. If the Arabs are correct in asserting that the land was theirs originally and it was stolen, then the question stands.

As for "Palestine" this term is typically interpreted one of two ways. The first way is to refer to all of the land in the British Mandate of Palestine which includes the Modern State of Israel (except for the Golan Heights), the Gaza Strip, and the West Bank. The second way is to refer to exclusively those territories which the Palestinian Authority claims will serve as a basis for a future Palestinian State: the West Bank and Gaza Strip (Palestinian Territories). Understandably, it changes the argument fundamentally if 78% of the territory in question is exempted from the discussion.

Legal Discussion
According to International Law, Israel exists as a legal and viable state with de facto borders along the 1949 ceasefire lines. The lands acquired in the Six Day War of 1967 are considered occupied-in-trust and should be devolved to Arab States as soon as a long-term peace deal is viable.

As for the 78% of Mandatory Palestine which is now the State of Israel, this came about through Israel's acceptance of UN Resolution 181 and its border defense against Arab aggression to counter international laws that they did not like. As a result, the acquisition in the 1947-1949 of war was not an illegal act since self-defense is not a criminal act unless it is grossly disproportionate to the attack and the war was a relatively balanced affair as well as being resolved at the moment that each Arab state was willing to engage in an armistice. Just to clarify, this means that the 1949 borders of Israel belong to Israel and since there was no act of theft, it is impossible to say how an act of theft occurred in this instance.

As for the Palestinian Territories, there is more of a discussion to be had. There are two general ways that Israeli Jews have acquired land in the West Bank in contravention to International Law. The first is urban expansion of Jewish residences beyond the 1949 boundaries (especially in Jerusalem) and the second is the establishment of settlements in the West Bank and formerly in the Gaza Strip. Israel has maintained the West Bank for over 40 years, which was far longer than originally contemplated in UN Resolution 181. Therefore, there is a question about whether Israel has the ability to negotiate urban planning in cities that were wholly or partially divided due to the armistice. Unfortunately, some areas of a city may gentrify, populations move and reorganize, and it is natural for Jews and Arabs to live in areas that they did not live in 40 years ago. This has resulted in some Jews buying Arab houses in up-and-coming districts and re-zoning in order to accommodate changes in the city.

As for the settlements, these are usually taken by a legal showing that the Palestinians living there do not actually own the land that they live on and that the Israeli Jews were able to purchase the land and construct on it. This is probably the most indefensible of the Israeli positions. The International Courts have clearly ruled against such settlements.

If the question is why nobody stops the Israeli Jews from doing this, this is rather straightforward. Most countries in the world care little for International Law in this regard enough to compel enforcement. Otherwise, Turkey would have to withdraw its occupying population from north Cyprus. Morocco would have to withdraw its occupying population from Western Sahara. The Indonesians would have had to withdraw their occupiers from East Timor prior to US military involvement. There are many other examples. Interestingly, Israel gets much more flack for its violations than these other actors which actually carted civilian populations into the territories as opposed to willingly letting their civilian population move around.