How do you identify adverbs in a sentence? Is there a rule?
You just ask a question first---how, when, where in a sentence.
Then you will have your answer; it is the basic rule to understand an adverb.
Marry has arrived at the airport safely.
Question was whether Marry arrived at the airport, HOW, safely or unsafely?
How? You have received the adverb that is indicating the verb ARRIVED.
Because,an adverb indicates/modifies always a verb, adjective or another adverb.
Once when I was living in Wang Chai ( Hong Kong), I saw many nationalities on the road everyday.
Look, at once----when question? again When --another a time question, double adverbs are used here to emphasize on a time issue.
Basic understanding of adverb has no problem at all.
You understand it easily. These are basic rules.
After learning them, you have to know advanced level of adverbs classification and placing of them, a bit more complicated that you implly here that I notice.
You need time to understand all, better follow Raymond Murphy, intermediate level. If you can understand them all, take advanced level book.