Nouns are the parts of the sentence that describe the person, place or thing, and are typically the subjects of the sentence. In the sentence, "The dog barked," the subject of the sentence is "dog," since it is a noun paired with a verb to describe what the subject of the sentence is doing. A noun may also be replaced by a pronoun, such as in the sentence, "She jumped when the dog barked."
Adjectives modify nouns in a sentence. They define the subject or the noun by answering, "which one," "how many" or "what kind." For instance, in the above sentence, "The dog barked," an adjective would describe what kind of dog it was. "The big dog barked." These adjectives almost always appear before the noun they are modifying. The exception to that rule are those adjectives that appear in a string of other adjectives, or appear before a pronoun. For instance, "The dog, which was big and scary, barked," is a case where the string of adjectives still define the dog, as opposed to the verb they precede.
The verb indicates what the subject is doing in the sentence. In the above sentence, "The dog barked," the verb indicates what the dog -- the subject -- is doing. Even if an adjective is required, such as, "The big dog barked," the adjective would modify the noun as opposed to the verb. Any single adjective used to modify the noun would seem out of place if used before the verb, because it would then attempt to modify the verb. At this point it would no longer be an adjective.
An adverb modifies the verb in a sentence, and generally always answers the question "how" in the sentence. In, "The dog barked," the question of how is not addressed. An adverb would specify that detail. "The dog barked loudly." In this case, and as a rule, adverbs are recognizable by the "-ly" at the end of the word. Unlike adjectives that are restricted to where they should fall in the sentence, adverbs can pop up at any point, even before a noun. "Suddenly the dog barked."