The train is moving quickly through the subway.

("Quickly" describes how the train moves. "Move" is a verb.)

The turtle is crawling through the grass very slowly.

("Slowly" describes how the turtle crawls. "Crawl" is a verb.)

He's usually late to work.

("Usually" is an adverb of frequency that describes an adjective--"late.")

He rarely buys things that are not on sale. He likes to save money.

("Rarely" is an adverb of frequency that describes the verb "buy.")

The water is very hot.

("Very" is an adverb that describes the adjective "hot.")

The water is too hot.

(very, too, really, so, extremely, etc. are adverbs that describe adjectives.)

She's entering the hot tub very carefully.

("Very" is an adverb that describes another adverb "carefully." The word "carefully" describes the verb, "enter.")