Whether paid-for or free, newsprint or electronic, newspapers are ephemeral - read today and in the recycling, lining the cat litter tray or disappeared into the ether tomorrow depending on the format. They provide a snapshot of the nation or local area at a particular time - politics, people, social events, gossip and soon forgotten.
Newspapers were first taxed in 1712 and the tax steadily increased as the UK government became concerned about the freedom of the press.
Newspapers became more popular in the mid 1800's when newspaper tax was repealed in 1855 and paper duty in 1861. This brought newspapers more within the reach of the wages of a working class household.
The ease of finding information in newspapers often depends what you are looking for and how you access archive copies. If you are looking for a particular event on a known date then looking through individual editions at a record office or on-line is not a great challenge - bearing in mind that a story that has a wider interest or curiosity value may be reported in newspapers outside the local area and some time after the event.
For a wider search for your place it is possible to go through edition after edition, page by page, but indexes are invaluable and will save a lot of trawling through page after page whether on screen, microfilm or physical newspaper.
There are a number of partial indexes on-line some are free, some paid-for and most national newspapers have paid for archives - the Times Index goes back to 1790. My county library allows users to access it from home and some libraries provide access from within the library. Part of the Times Index (Palmers Index to the Times) has been added to archive.org as part of Google Books
The most useful site is the British Newspapers Archive (http://www.britishnewspaperarchive.co.uk/). It is a paid-for site, but the index is free. When I looked for my place (New Fishbourne) there were over 5,000 entries ranging from 1750-1999 (with the majority in the 19th Century) with publications ranging from the "Aberdeen Journal" to the "Yorkshire Post & Leeds Intelligencer", of course with Sussex based newspapers listed somewhere in between.
Findmypast has a partial index of the British Newspapers Archives, but is also a paid for service (again check if available in your local library). Findmypast also has some Irish and US Newspapers included in the index.
Australian users have the excellent Trove site (http://trove.nla.gov.au/) which is free. For the USA, check the Free Newspaper Archives site (http://www.freenewspaperarchives.us/) as there are links to copies of a large number of mostly local newspapers.
So what can you find - as always it depends. For my site I have found reports of crime (theft, assault, bigamy, attempted murder), birth marriages and deaths, pastimes (flower shows, meetings, sports - the local football team lost against Havant), arrival of the railway (and some accidents), council rates, turnpike tolls (and reports of evasion), history of building the local waterworks, weather (and especially when extremes caused damage to property or people), the price of goods in the shops, obituaries and reports of funerals - the list is endless! Just try not to spend too much time reading the (archive) news, instead of working on your study 🙂