Nothing by dad is amongst first half of vulgar insults, initially that's what people say (3,6)

'people say' is the definition.
Although both the answer and definition are singular nouns, I don't understand how one could define the other.

'nothing by dad is amongst first half of vulgar insults initially that's' is the wordplay.
I cannot really understand how this works, but
'nothing' could be 'o' (O resembles 0) and 'o' is located in the answer.
'by' could be 'x' (as in 'multiplied by') and 'x' is located in the answer.
'dad' could be 'pop' (synonyms) and 'pop' is present in the answer.
'first' could be 'i' (I in Roman numerals eg Elizabeth I) and 'i' is present in the answer.
This may be the basis of the clue (or it may be nonsense).

'what' is the link.

Can you help me to learn more?