Funeral

A funeral is a ceremony to honor and pay respect to a person who has recently died, and typically involves arrangements for their corpse. Funerary customs are closely tied to religious beliefs and practices. Specific funerary practices vary throughout the known world, and can even vary within regions that follow the same religion.

Burial is the predominant method used in Westeros, by both followers of the Old Gods of the Forest and the Faith of the Seven, though cremation is practiced in certain locations. Meanwhile, cremation seems to be somewhat more common in parts of Essos, though burial is also practiced. The ancient Valyrians, (apparently) the Lord of Light religion, and the Dothraki all burn their dead on funeral pyres.

Faith of the Seven
In the Seven Kingdoms, the bodies of the dead are tended and prepared by the Silent Sisters, a religious order within the Faith of the Seven devoted to this task. Their monastic order is sworn to service of the Stranger, the aspect of the godhead that represents death and the unknown.

The body of the deceased is usually laid in state for visitors and prayers. The body is displayed atop an altar, changed into formal clothes (and if they died violently, their wounds cleaned up as best as possible). The body's hands are clasped together over the chest, and men's bodies are often laid in state with their hands clasping a sword (pointed down). In septs which are large enough to have statues of each of the Seven in a ring around the main chamber, such as the Great Sept of Baelor, the body itself is positioned so that the head is pointed towards the statue of the Stranger.

Two funeral stones are also placed over the closed eyes of the deceased, each painted to resemble open eyes. The symbolic meaning of this is to remind the faithful that they should not fear death, because it is not truly the end: we close our eyes in this world, but our eyes open again in the afterlife.

Wealthy adherents such as members of the nobility can afford to have their corpses embalmed, to slow the processes of decay while they are entombed. This process involves removing several internal organs from the corpse, the ones that break down most quickly, and placing them in seven ceremonial vases - which are then placed near the corpse at the funeral ceremony itself (often at their feet).

In King's Landing
As the royal family of the Seven Kingdoms, the remains of the members of House Targaryen, usually their ashes, were interred at the Great Sept of Baelor. Following the fall of the Targaryen dynasty, the new royal family was expected to follow in their footsteps, but King Robert Baratheon demanded his remains to be sent to his family's ancestral seat, Storm's End, to be interred.

Valuable servants of the crown sometimes may be deemed worthy of being interred at the Great Sept as well.

House Tully
The deceased members of House Tully are placed atop a wooden boat in the typical Seven Kingdoms fashion, including the death stones above the eyes and the canopic jars. The boat is also covered with straw and wood and then set down the waters of the Trident and set on fire with a flaming arrow.

In a mockery of House Tully's funeral customs, the body of Catelyn Stark is unceremoniously thrown into the waters of the Green Fork.

House Stark
The members of House Stark are traditionally interred in the catacombs of Winterfell, with a stone sculpture in the likeness of the deceased placed above the tomb.

The Night's Watch
The Night's Watch burn the bodies of their fallen members in funeral pyres. During the ceremony, the topmost sworn brother present recounts the life and actions of the deceased black brother. After the speech is over all the watchmen present say out loud "and now his watch is ended", in reference the sacred vow of the Night's Watch.

House Forrester
Deceased members of House Forrester are placed on an ironwood casket, with ironwood tree seeds in their palms. Their pyres are then burned, emitting the rare blue flame from the ironwood, that is said to only burn for Forresters.

Beyond the Wall
In the lands beyond the Wall the most common practice is to burn the bodies of the dead in funeral pyres. It is also practiced by the Free Folk as a form of protection, as burning a body prevents it from being raised as a wight by the White Walkers. Thus, the Free Folk burn the bodies of friends and foes alike.

The Dothraki
Similarly to the Free Folk, the Dothraki also burn the dead members of their own khalasars to ensure the entry of the spirit of the newly dead into the Night Lands to ride with his or her ancestors. Thus it is a major insult to leave a body unburned and mutilated, tantamount to "killing" the spirit of the recently deceased.

In the books
In the A Song of Ice and Fire novels, a few more details are given about funeral practices in different parts of the world.

The novels did not specifically mention that members of the nobility in Westeros have their bodies embalmed by removing several vital organs and placing then in seven vases with the corpse (somewhat like mummification). This was introduced in the very first episode of the TV series at Jon Arryn's funeral. At Tywin's funeral in the books, however, it is mentioned that his corpse was "embalmed" in some traditional fashion to slow its decay, so it seems to have been implied that something like this occurs in the novels. Showrunners Benioff and Weiss might not have been the ones who came up with this idea: in the Blu-ray commentary for the first episode, they openly express their confusion at what the vases near Jon Arryn's corpse are there for.

It hasn't been mentioned exactly what funerals are like for the ironborn, who follow the Drowned God - though it seems probable that they conduct burials at sea. Apart from the fact that they don't fear drowning and believe that they go to the Drowned God's watery halls when they die, the Iron Islands themselves have tough rocky soil which probably isn't conducive to burial, and they probably don't cremate their dead either, as it is stated that the isles don't have major forests so wood is relatively hard to come by as well.

In the Summer Islands religion, funerals are not somber occasions mourning the dead but celebrations of the lives they led, with wine and lovemaking.