Let's break down the sentence word for word:
- The = article
- children = noun (subject)
- excitedly = adverb (modifies the verb "talked")
- talked = verb
- about = preposition
- the = article
- fun = noun
- of = preposition
- fishing = noun
There's only one adverb and it is "excitedly" which modifies the verb "talked". It describes how the children talked. There are no adjectives in this sentence.
If the sentence said "they talked excitedly about big fish" then the word "big" would be the adjective that describes the noun "fish"; ie it elaborates more on the fish.