It is my understanding that seers were usually women, and that witchcraft was seen as a thing for women. However beyond that, I know nothing about how the ancient Norse practiced their religion, or if it there was any real dogma associated with it. On the show, however, the priests/seers are men, and there appears to be at least a little dogma associated with their religious practices. What do we know from history?
We've managed to piece together quite a bit about Norse religion, but there's still remarkably little information on the subject. Something important to keep in mind is that Norse paganism was by no means static, and we don't exactly know what version of paganism was practiced when.
Early Norse paganism (pre-793 CE or so) had many shamanistic elements, and the chiefs in local settlements, known as central places, were religious as well as political leaders. Priesthood was a vocation rather than a profession, and sorcery/witchcraft was known as seiðr. Seiðr was primarily associated with women, but there certainly are exceptions — it is said that Odin's power, for example, was derived from his seiðr spear.
Early Christian influence began in earnest in the 9th century, when missionaries like Anskar came to Scandinavia. Christianity had a significant impact on Norse paganism, and it may have altered pagan practices, even if Scandinavians did not convert. For example, the information we have on Ragnarök ("Fate of the Gods" or "Twilight of the Gods") closely parallels the Christian Day of Judgment. Another example is the story of the pagan Sigurd the Dragonslayer, which was later appropriated in Christian imagery, with Sigurd representing good and the dragon representing evil; originally, the morality of both figures was much more ambiguous.
As far as basic doctrine and sources go, Adam of Bremen writes about Norse paganism in his Church Religion (ca. 1072) and mentions that the three main Norse gods are Frey, Odin, and Thor. We do have reason to view this skeptically, though — having three male chief gods would be unusual for a pagan religion (consider the Roman Capitoline Triad, for example). Snorri Sturluson wrote the Prose Edda in the 13th century, but by this time, Norse paganism was long past its prime, so the accuracy of Snorri's work is also debated.
If you'd like more information, I'd recommend reading The Deluding of Gylfi from the Prose Edda ( http://hea-www.harvard.edu/ECT/carl_edda.html ). There are also plenty of books on the Viking World, such as The Viking Age by Anders Winroth. Almost all survey books will have chapters on Norse paganism and religion in the Viking Age.