In keeping with the ethnic and culturally bound nature of Asatru, those who wish to become Asatruar or Heathen must engage the cultures behind it. A study of the modern and ancient Germanic languages, a deep and introspective study of both history and the sacred stories of the Heathen world, and a real and transformative effort to live one's life by the moral and ethical ideals behind Asatru as well as a personal identification with the Heathen religious culture are all required to some extent before one can be said to have become a "believer in the Gods".
Asatru is an organic religious tradition, not a revealed religious establishment with a central doctrinal authority or hierarchy. Groups of Asatruar are organized locally, following unique local customs. Each member of the faith is enjoined to study the Ancestral lore for guidance in living, and to build strong communities of friends and faithful to have a taste of what real communal spiritual life is like, and what it was like centuries ago.
Like the historical Heathens, Asatru rejects the idea of "spiritual authorities"- there is no "bible", or any other authoritative documents that bind all Asatruar, but there are sacred stories and traditions that come down from the past, giving advice and examples for living rightly with the Gods and others. How a person or a community interprets them is largely a matter of their own insight and conscience.
Recommended reading (pdf e-books):
Aleister Crowley - The Heart Of The MasterJohn Earle - The Deeds Of Beowulf
Michael Smith - Ways Of The Asatru