Longman Grammar pp. 193-196, 204-208, and 218 discusses the formation and syntactic roles of adverbs. You can find the characteristics of adverbs as a word class summarized briefly on pp. 22-23 and those of adverb phrases on p. 44.
Here, you can find a concise presentation of (A) the structure of adverb phrases with the types of pre- and postmodifiers that can precede or follow adverbs, and (B) the most common syntactic functions/roles of adverb phrases.