This is going to be a very difficult question to give a short answer to, because we're talking about a breadth of time (from Pre-History and the Bronze Age through Iron, Migration, and Conversion) and an expanse of geography (from England up to Scandanavia, down into France, and as far east as parts of Russia.)

Tacitus tells us there were priests, but by the time of Pagan Iceland, cultic practice sort of defaulted to community chieftans called Goðar, which acted both as priest and chief.

For the ancient stuff, Dumezil and Bruce Johnson are my go to's for Proto-Indo-European reconstruction. I quite liked David W. Anthony's "The Horse, the Wheel, and Language."

For later stuff, Jon Hnefil Aðelstainsson's Under the Cloak is a good examination of the conversion of Iceland. Simek's "Dictionary of Northern Mythology" is a good reference to have.

To get a sense of the cultural zeitgeist of the Germanic Peoples, I would recommend Culture of the Teutons, by Vilhelm Grönbech, which remains one of my favorite ethnographic treatments of the subject. One thing to remember is that there is no separation of religious life from cultural life. They are one in the same.

The Germanic religion was the Northern expression of the Indo-European Religious family. As such, it holds some similarities with Roman, Greek, Celtic, Vedic, Hittite, and other religious traditions. At the core of them all was a Client-Patron relationship with the divine, where the people where given blessings in the form of would be called Luck, and the Gods were given sacrifices in the form of material goods and living beings (usually livestock, but human sacrifice is recorded, particularly among the Germans.)

In addition, the Germans also believed in a metaphysical system of Causality usually expressed as Wyrd, or Fate. They put a lot of stuck in being able to read the trends and be able to predict the future, through Augury, bird sign, and the neighing of horses. Horses were very important to the Germans, as a reflex of the PIE Horse and Chariot culture.

HR Ellis Davidson's Myths and Symbols; Priscilla Augustyn's Semiotics of Fate, and Kris Kershaw's The One Eyed God also gives very interesting aspects of Germanic Belief.