Aninut (אנינוּת) is the first of the Jewish mourning stages, and it lasts from the moment of death until the body is buried.

Mourners during this stage are called "onen" and are not expected to perform normal daily Mitzvot (commandments) during this time.

During Aninut, the body of the deceased is never supposed to be left alone. Rather, it should be guarded by a Shomer or Shomeret (literally a guard). Shemira is a sign of respect for the dead, in ancient times this was a literal guard to avoid rodents or other animals eating the flesh, but today it is more of a symbolic act of accompaniment. Performing shemira is considered a mitzvah. 

Halvayah (הַלְוָיָה), or the funeral, is supposed to happen as soon as possible after the death- often within twenty-four hours.

Mourners come to the funeral to recite prayers, eulogize the deseaced, and tear their clothes as a sign of their mourning. The funeral may occur in a synagogue or home, and then funeral-goers accompany the body to the cemetary.

After the body is lowered into the ground (generally in a white shroud or plain wooden coffin), everyone in attendance helps to bury them by throwing dirt over the grave. Some mourners may use the back of the shovel at first to demonstrate reluctance. In some communities, each mourner replaces the shovel back in the earth rather than hand it directly to the next person.

Immediately on returning from thecemetery, mourners should be greeted with a “meal of consolation.”

Shivah (שִׁבְעָה) is the seven day period following the burial (which pauses for Shabbat) during which family and community visit mourners to bring them food and comfort. In English, this custom is often called "sitting Shivah." Mourners during this time are called "avel."

 There is often a service held in the mourners' home so that they can say the Mourners' Kaddish, which requires a minyan (a group of ten adult Jews).

The shiva period gives the mourners a time to withdraw from the business of the world and begin to integrate and accept their loss. At the close of shiva, friends or family traditionally accompany the mourner for a brief walk to symbolize the start of re-entry into the world.

Shloshim (שְׁלוֹשִׁים‎) is the first month (thirty days) from death, during which mourners may resume daily activities. During this period, mourners often still refrain from cutting their hair, listening to live music, or attending other public celebrations.

Shloshim eases the mourners back into normal routines without forcing them to completely integrate into the world. During Shloshim, mourners still say the Mourner's Kaddish every day - generally at temple. After Sheloshim (on the thirtieth day) a memorial service is often held, which is similair to the funeral.

Shloshim marks the end of the mourning period for all relatives except for parents of the deceased. Although many people believe and even behave otherwise, after sheloshim the Mourner’s Kaddish is no longer traditionally recited for a spouse, sibling, or child. All mourning restrictions are lifted.

Matzeivah (מצבה) is the formal ceremony of unveiling the gravestone at the cemetery. It is traditionally held after Shloshim but before the first Yahrzeit (anniversary of passing) - often within the twelfth month.

The ceremony is generally pretty breif, including some psalms and prayer as well as reflections on the deceased and their lives.

After the unveiling, the family of the deceased often returns to the grave on Yahrzeits and around the high holy days. When visiting the grave, it is customary to place a stone on the grave.

Yahrzeit (יארצייט) is the Yiddish word for the anniversary of someone's passing. Yahrzeit is often observed according to the Hebrew calendar. 

On someone's Yahrzeit, a 24-hour yahrzeit candle is customarily lit in memory of the deceased. There is no prayer for this candle, althogh it is often accompanied by reflections and readings, as well as recitation of the Mourners' Kaddish in a minyan (a group of 10 adult Jews). 

Yitzkor (יזכור) is the memorial service held on Yom Kippur, Pesach, Shavuot, and Sukkot. Yitzkor is an Ashkenazi custom.

It is customary for those with both parents alive to leave the main sanctuary during the Yizkor service, out of respect or superstition. It is usually not attended within the first year of mourning, until the first yahrzeit has passed. The Yizkor prayers are intended to be recited in a synagogue with a minyan; if one is unable to be with a minyan, one can recite it without one. Still, this practice is a custom and historically not regarded to be obligatory.

JCFS guide to TRADITIONAL JEWISH RITUAL AND MOURNING PRACTICES.

MyJewishLearning.com

Wikipedia