In Emily Dickinson's poem "He ate and drank the Precious words", the tone of the poem is brought forth by the message of the poem.
Mood is defined as by the emotion the text brings out in a reader. Therefore, the mood of a poem can change from reader to reader. This happens because no reader is the same person, with the same personal history, and the same emotions.
Therefore, the answer to the question will reflect what I believe to be the mood of the poem based upon my subjective thought.
The mood of the poem is one of elation (or happiness). The book that the man reads brings him to a metaphoric intoxication. It is through this 'drunkeness' that the man is able to forget his past and current problems. The book (which many have assumed to be either the Bible, or a text similar to the Bible) allows the man to find a new happiness:
Was but a book. What liberty
A loosened spirit brings!
The mood is simply established, for me as the reader, through the recognition that one can find true happiness and forgiveness somewhere.