Source: AWOIAF
The Seven
Across much of Westeros, especially south of the Neck, the primary religion is that of the Seven. Though some people worship the Father, Mother, Warrior, Smith, Maiden, Crone, and Stranger as separate entities, in truth the Faith of the Seven is a single deity with seven aspects or "faces".
As the name suggests, the number seven is integral to the Faith of the Seven. From The Seven-Pointed Star - the holy book of the Faith, to anointing with seven oils when raising a Knight, to the seven-sided Septs where the faithful pray, the number seven is a constant factor.
Male Septons and female Septas are the primary attendants of the Faith. Septons generally tend a Sept, with occasional visits to neighbouring towns, while Septas frequently take employment amongst the nobility as governesses to the daughters of Lords. Also fairly common (though unpopular) are the Sparrows, men and women of the Faith who have taken vows of abject poverty. They travel from place to place, preaching the Faith, and living on the charity of the faithful.
A smaller, but vital segment of the Faith is the Silent Sisters, these women are called upon to perform the sacred preparations that are required by the Faith when a person dies. Much less common is the Faith Militant. Since being outlawed more than two centuries ago, the faithful warriors have either laid down arms, or taken on more subtle roles.
The Faith of the Seven holds guidelines for most aspects of life, but is most important when it comes to marriage and death. The Faith prohibits prostitution, gambling, bastardy (though apparently not adultery), and polyamory; though only the most committed adherents actually seek to root out and outlaw the existence. Slavery and incest are considered abominations, and kinslaying is the greatest betrayal one can commit.
The Old Gods
North of the Neck, worship of the unnamed and uncounted Old Gods remains common. Worship of these nature deities was taught to the First Men by the Children of the Forest, the mystical elf-like beings that lived in Westeros before men came. The faith of the Old Gods is less strictly codified, though slavery, incest, and kinslaying are offensive to the Old Gods as well. The tenets of the Old Gods generally relate to honestly and "honour".
Worship of the Old Gods is done outside, in groves of trees known as Godswoods. The oldest of these include a Heart Tree, an ancient weirwood that has been carved with a face. It is said that a Heart Tree knows when a man tells a lie, and for this reason oaths and vows, including that of marriage, is done before a Heart Tree. A Godswood does not, by definition, require a Heart Tree - or even any weirwood at all - but adherents of the Old Gods commonly find the notion uncomfortable.
North of the Wall, the Wildlings are said to worship an even older form of this faith.
The Drowned God
The Iron Islands practice their own faith, dating back to before the Andal Invasion brought the Faith of the Seven to Westeros, and it is possible that the Drowned God is a singled-out deity from the pantheon of Old Gods. The Ironborn believe that they were created by the Drowned God in his image to rule over the all the waters.
The Drowned God has no temples and no holy books, but is maintained by oral tradition. Priests braid their hair with seaweed and carry a skin of seawater to bless the faithful with. All Ironborn are baptised in sea water. For newborns this may involve little more than a splash of seawater, though grown men are submerged in the sea until they cease breathing, after which a priest attempts to revive him.
A death at sea is considerable honourable, and a drowning a blessing from the Drowned God himself. The Ironborn believe that upon their death, they descend beneath the waves to serve their god.
R'hllor
All but unknown in Westeros, the faith of the Red God was brought to Westeros by the Rhoynish, finding a small foothold in Dorne, but little more. For the nobility beyond Dorne, the worship of R'hllor is little more than a strange rumour or foolish pagan custom, if they have heard of it at all. In the Free Cities of Essos, Red Temples are prominent features, but none exist in Westeros.
Unlike the Westerosi religions, men and woman are treated equally in the faith of R'hllor. Prostitution is permitted, and even encouraged, with many Red Temples having trained prostitutes alongside Priests and Priestesses.
Beyond the Narrow Sea
Essos, the Dothraki Sea, and beyond have numerous gods and practices, and many more than have since faded from memory. Religious study may be undertaken by acolyte maesters at the Citadel, but interest in such things is generally considered deviancy amongst the nobility of Westeros, while the Smallfolk have simply no time for such things. Gossip about the absurd beliefs of the backwards people beyond the Narrow Sea would not be considered appropriate dinner table talk, but it might find some traction amongst the cultured wanting to impress, though it is likely to be utterly inaccurate.
A Maester who has not forged a link in religious studies would generally know about R'hllor, Mother Rhoyne, the Horse God worshipped by the Dothraki, the Shepherd of the Lhazareen, and the Weeping Woman of Lys. They would also know of the Many-Faced God, whose worshippers believe that all gods are, in fact, Him of Many Faces.
Closer to home is the Merling King - generally considered apocryphal, though his is depicted on the Manderley coat of arms - and that a number of Targaryen dragons were named after ancient Valyrian gods.
