Adverb phrases and clauses answer the same questions that Adverbs do: "How?" "When?" "Where?"
When a group of words NOT containing a subject and verb acts as an adverb, it is considered an adverbial phrase:
Correlative Conjunctions, Prepositional Phrases, and certain Infinitive Phrases all have the potential to be adverbial phrases. An adverbial phrase, therefore, should not be thought of as a particular part of speech but, rather, as the collective function of a group of words composed of other parts of speech. That function would be shown in a sentence diagram by placing the phrase diagonally under the word or words it modifies.
In the diagram above, note how all of the phrases are in service to the idea that budgets “have changed.” Consequently, they all come under that one verb, in some fashion, and are therefore adverbial.
In similar fashion, an entire clause--a group of words containing a subject and verb--can begin with a Subordinating Conjunction and modify Verbs and Verbals in other clauses. These are adverbial clauses. The subordinators tend to indicate how, when, where, and sometimes why.
There's no trick to diagramming them. The subordinating conjunction goes on a dashed diagonal line connecting the verb or verbal to the subordinate adverbial clause: