The child has to declare interest in acquiring Portuguese nationality, provide own ID and that of the Portuguese parent, proof of effective connection to the portuguese community (what is considered proof of connection to the community has changed somewhat recently), language competence, clear criminal record after 16 years of age, etc. Briefly, the child can apply for naturalisation based on the link to their Portuguese parent.
I have edited this post to provide a better link to the requirement for children under 18 whose parent acquired Portuguese nationality after they were born: Como obter a nacionalidade portuguesa the proof of “effective link to the portuguese community” is conceded if the child has residence in Portugal for 5 years. The parent can then sign the declaration that the minor wishes to acquire Portuguese nationality.
This thread which has links is relevant.
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