Okay, here’s my long thing now that I’ve done the short-tempered reconstructionist obligatory gromph at the bloody Rede.
“Pagan” is pretty much a none-of-the-above religious term category; the only definition of what it means that isn’t liable to irritate some pagans is that a pagan is a follower of a non-Abrahamic religion. As soon as someone starts adding more to that, some pagan religion or another winds up dropped out of the system, and this makes for crankiness all around. (Some of the popular ways of irritating people: the word or concept of ‘earth-centered’ or ‘earth-based’; belief in the Wiccan Rede or Threefold Law; Lord-and-Lady belief-set or talking about The Goddess (tee-em).)
There are three broad categories in modern paganism, plus a bunch of miscellaneous things that don’t categorise easily. Those are: 1) the religious witches (best known are Wicca and its derivatives); 2) the people whose stuff derives from various magical societies (such as Thelema); 3) the reconstructions (of which the best known is Asatru). For the miscellaneous random shit, you wind up with some Discordians, some but certainly not all African Diaspora religious practitioners, various people primarily influenced by various polytheistic, pantheistic, shamanic, or animistic extant religions (tribal religions, Hinduism, and Shinto are the ones I’ve seen most often). You also get people who do combinations, eclectic things (most eclectics are most similar to category #1), and incorporate things like New Age beliefs into their religions.
Most pagan religions do not have sacred texts in the sense of having revealed scripture. However, many have other written materials. Wicca has what is referred to as a ‘Book of Shadows’, which is the recorded lore that a new member of the religion acquires in their study. The Thelemites have the esoteric ramblings of Crowley to gnaw on. The various reconstructions have surviving material – the Greeks have, of course, the plays and renditions of the myths, many of which were sacred performance in their time (though never holy writ); the Egyptians have the vast storehouse of written material, far more than we’ve translated, much of which is talking about sacred subjects. On the other hand, most of the northern Europeans don’t have much written material to work with at all, and essentially none that is before the Christianisation of the regions.
I can speak more specifically on two pagan religions: the Kemetic (Egyptian reconstruction) and Feri witchcraft:
The essential concept in Kemetic religion is the concept of ma’at. If you’re familiar with the standard Egyptian afterlife art, ma’at is the feather against which the heart is weighed at judgement. It’s one of those hard-to-define ideas, encompassing “truth”, “justice”, “order”, “right action”, “right relationship”. It is the responsibility of all beings to uphold ma’at; I tend to think of this as taking a stand against entropy. We believe that this is not a fallen universe or one that needs redeeming, but it definitely needs maintenance, because otherwise it will run down from the perfection of creation. This maintenance includes not only right relationship with the cosmos/gods/what have you, but also a strong, mutually supportive community and healthy individual people.
Kemetics range from fairly strong but not perfectly hard polytheists through to those who believe in an ultimate god-behind-god (to nick a line from Borges here) Whose manifestations are the gods we know. (This latter structure is common in African religions.) Personally, I am about as strong a polytheist as what we know about the ancients can justify. Whether monolatrist or polytheist, a recognition of the diversity of the created world is important, as well as an awareness that the gods appear in many forms.
Kemetic basic ritual includes cool water libations, the lighting of a candle or candles, and burning incense or scented oil. Offerings are made to the spirits of the ancestors, to the gods, and to other denizens of the unseen. Those offerings are treated like offerings in Hinduism, as a shared meal between the god (or whoever) and the worshipper; no part should be wasted. For this reason, most Kemetics do not make offerings that they or someone in their household cannot consume, even if those are traditional ones to make. (I know someone who does not make any alcohol offerings, because she does not drink, for example.) The use can vary; I know people who have given their offering water to their pets (especially in the case of cat owners who are devoted to Bast) or used it to water plants, as well as the more traditional drinking thereof.
There are more specific beliefs particular to denominations of Kemetics; I cannot speak to these personally because I am nondenominational. These include varying beliefs on the importance of having a spiritual leader in an equivalent role to the divine king of ancient Egypt, the nature of the personal relationship between the gods and their followers, and similar matters.
Most Kemetics will be particularly devoted to a subset of the pantheon, but will also acknowledge the other gods in Their appropriate places. The ones I personally follow are Hathor, Khnum, Wepwawet, and Set.
Feri witchcraft is a form of American religious witchcraft coalesced into its present-day form primarily by the late Victor Anderson and his wife Cora. The word “Feri” is a shifted spelling of “Fairy”, and you will see some people using other spellings as well; this has led to some conflatings, some of which apparently frustrated Victor in his lifetime. (He has been quoted to me as saying something like, “If I’d known fairies were going to be so popular I’d have named the damn tradition something else.”)
To those familiar with the commoner forms of pagan practice, the Feri basics will be familiar: rituals are held in a space sanctified for the occasion, though Feri practitioners use a sphere, not a circle; many of the tools (blade, cup, wand, cauldron) will be familiar; members of the religion will refer to themselves as witches. Like Wicca, Feri is an initiatory religion, and thus the information which is publically available is not complete.
The Feri pantheon begins at the Star Goddess, Who is creator and ground of all being; She is all that is, pervasive in everything. Her children are the Twins, Who have many forms, male, female, both, and other; They were born in the Star Goddess’s first orgasm, which was the flash of initial creation. When the Twins, who are lovers and opposites, unify to reveal the path of integration, there is the Peacock God, Whose feet are in Hell and whose tailfeathers reach to Heaven, Who makes the seven heavens shake with His thunder.
The goal of Feri as a religion is to achieve realisation of one’s full potential, which includes the apprehension of one’s place as part of the divine. It is explicitly queer and polygendered; the ability to recognise both male and female in oneself is a part of the instruction process. (As a result of this, there are many gay and bisexual Feri practitioners, as well as other people who are uncomfortable with the gender duality of much religious witchcraft. The fact that all healthy sexuality is valued in Feri is also an appeal.) Creativity is highly valued; Victor Anderson frequently taught with poetry. The woman I am studying with teaches with dance.
The Cauldron’s Pagan Primer at http://www.ecauldron.com/newpagan.php can give you a sense of overview of more religions than are liable to come up here. I wrote the Kemetic FAQ there.