Adverb describe (modify) verbs and other adverbs. When looking for an adverb, you must first find the verb. In the first sentence, the verb is took. Off is also an adverb, but ask yourself, took off "how"? If you can answer that (with quickly and cautiously), that is your adverbial phrase. From an overnight rain, over the surface, and around the track are all prepositional phrases. Warm and shining are describing the sun, so they are adjectives.
