The largest collection of Newspapers in the UK is at the British Newspaper Library, Colindale, London.
Most County Record Offices or Local Studies Libraries hold copies of Newspapers of their area usually on microfilm.
Newspapers began to appear in the late Seventeenth Century and became more widespread in the early Eighteenth Century. From around 1750 onwards regional Newspapers started to report local events and references to individuals became more common.
Resourcing older Newspapers can seem hard work at first. The print is often small and the accounts sometimes appear stilted and formal. However, with some persistance the rewards can be great.
Your ancestors may appear in accounts of local interest - births, marriages, deaths, burials, funerals, obituaries were announced or reported in some detail. Possibly your Ancestor was reported as bankrupt or maybe had a mention of a role in the Church or other organisation. Those with Ancestors in trouble with the law and they appear in many Family Trees will find plenty of references to crimes commited and Court cases. Accounts of Court Cases are often fuller in Newspapers than in formal Court records. Those sentenced to transportation often for minor petty repeat offences are reported. Accounts of those sentenced to death and later executed are reported in great detail reflecting the fascination there was of reporting someones final moments.
During Wars Newspapers report those killed or missing as well as medals awarded.
Indexes to local Newpapers are rare although it is worth checking with County Record Offices or the National Newspaper Library as some names and topics may have been indexed by enthusiasts. There is a record at the British Newspaper Library of all indexes to local and National Papers they are aware of.
The Times National Newspaper began to be indexed by C.J Palmer in the 19th Century from 1790. This index although useful isnt fully comprehensive. From 1907 the Publishers produced an Official index which is more comprehensive. The Gentlemans Magazine 1731 - 1908 has been well indexed. You can locate an entry, discover the date and cross reference other local or National Newspapers perhaps for a fuller account of an event involving your Ancestor
Even if your Ancestors do not appear in Newspaper accounts they are well worth reading as they report news as it happened at the time and give a flavour of the time and place your Ancestors lived in.
Philip Westwood runs a genealogical service enabling Americans and Canadians to research their English Ancestors. For more details view his profile.