Since Heathenry is a living faith of active practice, the best place to start is always with a good local group, a kindred of kindhearted people open to teaching you. To find a good kindred, ask around among your pagan community or attend a regional Heathen gathering, a moot. Go to a Pagan Pride Day in your area, stop in at the metaphysical shops and book stores, and look for websites and Facebook pages for nearby groups, especially those who offer teaching and community outreach or participate in larger events.
Not all kindreds are open to the public, however, (some require oaths or sponsorship to participate in rites) so be patient. Heathenry is also not a monolith of organized creeds: local customs, forms of ritual, style of organization and even the Gods we worship within the Norse pantheon differ from person to person and kindred to kindred. Some groups are reconstructionists, focusing on the practices known from history and archaeology; others are open to a more modern, experiential-based practice.
Primary Sources - Know your Eddas, History & Archaeology
Heathenry and Asatru are not text-based faiths, nor are they limited to Scandinavian practice. Our sacred stories, beliefs, magical practices and customs are recorded in the literature, archaeology, oral lore and histories of countries across the Northern Hemisphere, from Greenland to Russia (and also, surprisingly, the US!). Sources include folklore, sagas, mythic lays, poetry and song, charms, children's games, fairy tales, local holidays and historical writings.
The most famous primary sources are the Poetic Edda, (a compilation of ancient lays recorded in Iceland, often seen as more purely pagan), and the Prose Edda, (a novel-like book of myths and the stories behind phrases used in poetry), written by Snorri Sturleson, a medieval Icelandic politician and poet. After much comparative study of the Norse diaspora, I also rely on multiple fairy tales recorded by the Brothers Grimm, and books of folklore from Scandinavia, Poland, Scotland and more.
Historical sources have to be read gently, understanding the cultural, religious and political agenda of the times, often tainted by hostility against their subject. These include Germania by the ancient Roman writer Tacitus, the medieval chronicles of Christian clerics Saxo Grammaticus and Adam of Bremen, writings by Byzantine historian Procopius (History of the Gothic Wars) and the records of Ibn Fadlan, an Islamic traveler to the state of Kievan Rus (early medieval Russia).