Newspaper content may be in copyright, or out of copyright:
In case of newspapers fair dealing applies:
Anybody can copy an 'insubstantial part'. This is not defined in law, but almost certainly precludes anything materially useful by itself. A single copy, in any format, of a 'substantial part' may be made under fair dealing for private study or for research for a non-commercial purpose, and the generally accepted upper limits of what constitutes a substantial amount that can be copied within fair dealing are as follows:
Any more than this is probably not fair dealing. Nor is it fair dealing to copy, say, one article from a book or journal on one occasion and another article from the same book or journal on another occasion. Note also that introductory and similar matter are not excluded, but should be treated as chapters or articles.
A library may make and supply to you a copy, in any format, of part of a published work within the same limits. The librarian will ask you to complete a copyright declaration, which limits your use of the copy to private study or non-commercial research.
To know whether a newspaper article is out of copyright, you need to know if the article was signed or not. According to British Library guidance, if the article is unsigned, copyright expires 70 years after publication; if the article is signed, copyright expires 70 years after the death of the author.