You construct a compound verb out of an auxiliary verb and another verb.
In particular, you may use an auxiliary verb (also known as a helping verb) with the verb in order to create the many of the tenses available in English.
In each of the following sentences, the compound verb appears highlighted:
Karl Creelman bicycled around the world in 1899, but his diaries and his bicycle were destroyed.
The compound verb in this sentence is made up of the auxiliary "were" and the past participle "destroyed."
The book Seema was looking for is under the sofa.
Here the compound verb is made up of the auxiliary verb "was" and the present participle "looking."
They will meet us at the newest café in the market.
In this example the compound verb is made up of the auxiliary verb "will" and the verb "meet."
That dog has been barking for three hours; I wonder if someone will call the owner.
In this sentence the first compound verb is made up of the two auxiliary verbs ("has" and "been") and a present participle ("barking"). The second compound verb is made up of the auxiliary verb "will" and the verb "call."