What will happen prior and after the End of Days? What are the stages leading up to this moment and what kind of events or happenings do they contain?
I try to get a clear view on the Jewish view on concepts like the Yemot HaMashiach (days of Mashiach), Techiyat Hametim (resurrection) and the Olam Haba. http://www.jewishencyclopedia.com seems to declare the End of Days equal to the Day of Judgement (Yom HaDin) and the Day of HaShem.
I only want to add to @mbloch's answer three very important principles (in my view) of Rambam's (Melachim 12).
"All these and similar matters cannot be definitely known by man until they occur for these matters are undefined in the prophets' words and even the wise men have no established tradition regarding these matters except their own interpretation of the verses. Therefore, there is a controversy among them regarding these matters."
"Regardless of the debate concerning these questions, neither the order of the occurrence of these events or their precise detail are among the fundamental principles of the faith. A person should not occupy himself with the Aggadot and homiletics concerning these and similar matters, nor should he consider them as essentials, for study of them will neither bring fear or love of God."
"Similarly, one should not try to determine the appointed time for Mashiach's coming. Our Sages declared: 'May the spirits of those who attempt to determine the time of Mashiach's coming expire!' Rather, one should await and believe in the general conception of the matter as explained."
To your question what to expect in those days, I think the Gemora in Soytah 49b gives some glimpses:
"בעקבות משיחא חוצפא יסגא ויוקר יאמיר הגפן תתן פריה והיין ביוקר ומלכות תהפך למינות ואין תוכחת בית וועד יהיה לזנות והגליל יחרב והגבלן ישום ואנשי הגבול יסובבו מעיר לעיר ולא יחוננו, וחכמות סופרים תסרח ויראי חטא ימאסו והאמת תהא נעדרת נערים פני זקנים ילבינו זקנים יעמדו מפני קטנים בן מנוול אב בת קמה באמה כלה בחמותה אויבי איש אנשי ביתו פני הדור כפני הכלב הבן אינו מתבייש מאביו ועל מה יש לנו להשען על אבינו שבשמים "
Translation: "In the times of the approach of the Messiah, impudence will increase and high costs will pile up. Although the vine shall bring forth its fruit, wine will nevertheless be expensive. And the monarchy shall turn to heresy, and there will be no one to give reproof about this. The meeting place of the Sages will become a place of promiscuity, and the Galilee shall be destroyed, and the Gavlan will be desolate, and the men of the border shall go round from city to city to seek charity, but they will find no mercy.
And the wisdom of scribes will putrefy, and people who fear sin will be held in disgust, and the truth will be absent. The youth will shame the face of elders, elders will stand before minors. Normal family relations will be ruined: A son will disgrace a father; a daughter will rise up against her mother, a daughter-in-law against her mother-in-law. A man’s enemies will be the members of his household. The face of the generation will be like the face of a dog; a son will no longer be ashamed before his father. And upon what is there for us to rely? Only upon our Father in heaven. "
For even more dreadful predictions please read Sanhedrin.97a Hope it helps.
There are two understandings of olam haba, the world to come, one in the context of where the neshama (Jewish soul) goes after the body's death, the second in the context of the arrival of Mashiach (the Messiah).
The traditional chronology for the arrival of Messiah which links the ideas of your question (end of days, resurrection and the olam haba) as explained by the Rambam (Law of Kings 11:1) is as follows (taken from chabad here)
Moshiach will first rebuild the Temple and then gather in the exiles. Jerusalem and the Temple will be the focus of divine worship, and “from Zion shall go forth Torah, and the word of the L‑rd from Jerusalem.”
The Sanhedrin — the supreme Jewish law court of 71 sage s —will be re-established, and will decide on all matters of law. At this time, all Jews will return to full Torah observance and practice. [...]
The Talmud discusses whether miracles will happen and again arrives at the conclusion that, if we are meritorious, the messianic redemption will be accompanied by miracles. However, the realization of the messianic dream, even if it takes place naturally, will be the greatest miracle.
According to some traditions, G‑d Himself will rebuild the third Temple. According to others, it will be rebuilt by Moshiach; still others suggest a combination of the two opinions. Some suggest that there will be two distinct periods in the messianic era: first a non-miraculous period, leading into a second, miraculous period.
What will become of the world as we know it?
Initially, there will be no change in the world order, other than its readiness to accept messianic rule. All the nations of the world will strive to create a new world order, in which there will be no more wars or conflicts. Jealousy, hatred, greed and political strife (of the negative kind) will disappear, and all human beings will strive only for goodness, kindness and peace.
In the messianic era there will be great advances in technology, allowing a high standard of living. Food will be plentiful and cheap.
However, the focus of human aspiration will be the pursuit of the “knowledge of G‑d.” People will become less materialistic and more spiritual.
Maimonides writes, “Neither the order of the occurrence of these events nor their precise detail is among the fundamental principles of the faith . . . one should wait and believe in the general conception of the matter.”
Following that first Messianic area, comes the resurrection area
[Following Moshiach arrival and the rebuilding of the Holy Temple in Jerusalem,] the ingathering of all the exiles will then follow. The resurrection of the dead will occur forty years after the exiles return to the Land of Israel. Tzaddikim, the saintly righteous men and women of the generations, are an exception to this rule; they will be resurrected immediately with the arrival of Moshiach.
First the dead who are buried in Israel will rise from their graves, they will be followed by the dead of the Diaspora, followed by the generation that left Egypt and died in the desert. Last of all will rise the Patriarchs and Matriarchs. Their resurrection is postponed so that they should have the nachas of waking to find all their children alive, well, and happy.
The categories mentioned above will also be further subdivided. The more righteous individuals will be resurrected before the general population. Amongst these righteous individuals, those who were primarily preoccupied with Torah study will take precedence over those whose forte was mitzvah observance.
For further reading see e.g., here on MiYodeya and here.
The arrival of the Messiah: According to Jewish tradition, the Messiah will be a righteous descendant of King David who will come to redeem the Jewish people and bring about the final redemption. His arrival will be accompanied by great signs and wonders, and he will gather the Jewish exiles back to the land of Israel.
The rebuilding of the Temple: Once the Messiah arrives, he will oversee the rebuilding of the Holy Temple in Jerusalem, which was destroyed by the Romans in 70 CE. This will be a time of great joy and celebration, as the Jewish people will be able to offer sacrifices and perform other rituals in the Temple once again.
The resurrection of the dead: After the Temple is rebuilt, the Messiah will bring about the resurrection of the dead. According to Jewish tradition, this will involve the physical reanimation of the bodies of the deceased, who will then live forever in the Messianic era.
The final judgment: Once the dead have been resurrected, there will be a final judgment in which God will judge all people and reward the righteous and punish the wicked. This judgment will be based on a person's deeds and the state of their soul at the time of death.
The establishment of the Messianic era: Following the judgment, the righteous will enter into a new world of peace and harmony, where the lion will lie down with the lamb and all nations will recognize the one true God. This will be a time of unprecedented spiritual and material prosperity, and the world will be filled with the knowledge of God.
Sources for these beliefs can be found throughout Jewish texts, including Isaiah 11, Ezekiel 37, and Zechariah 14 in the Tanakh, as well as various passages in the Talmud and Midrash. Jewish mystics, such as the 16th-century Kabbalist Isaac Luria, also wrote extensively about the eschatological process and the role of the Messiah in bringing about the final redemption. It should be noted, however, that there is no one authoritative source for Jewish eschatology, and there are many different interpretations and variations on these beliefs within Orthodox Judaism.
