Guide to Genealogy
In the first instance, from your parents, obviously. And if you're unaware of how that works, we're certainly not going to be the ones to tell you. If you are looking a little further back, however, to establish whether your ancestors came over with William the Conqueror, or Julius Caesar, or simply on a package holiday prolonged by amnesia, you might appreciate the assistance of one or more of the fine organisations listed below.
Genuki: UK & Ireland Genealogy is a good starting point for general advice. This site will help you to find out what can be found out and what can't. Other options include the Directgov website, for births, marriages, deaths, adoptions and civil partnerships, The National Archives for census returns, wills, military records and more and the UK Government Web Archive for an archived version of FamilyRecords.gov.uk (which we used to link to here).
Cyndi's List, "your genealogy starting point online for more than a decade", is also popular. Several hundred thousand links constitute one lady's personal attempt to organise online resources on genealogy.
On a slightly less cheerful note, you may be concerned to establish not the distinguished lineage of your relatives, but instead the last resting place of their mortal remains. The Commonwealth War Graves Commission is the organisation to contact. Records of 2 million graves from both world wars and details of 60,000 civilians who died in the second world war are available.
Other sites include Ancestry.co.uk (family tree, genealogy and census records - compile your family tree online; they do the searching for you), Familysearch.com (international results), Origins.net (80+ million British and Irish records dating back to the 13th century), the Society of Genealogists and College-of-arms.gov.uk (official repository of the coats of arms and pedigrees of English, Welsh, Northern Irish and Commonwealth families and their descendants). Please note that many of these sites will charge for their services.
Locally, the Oxfordshire History Centre in Cowley is an incredible resource of transcripts of parish registers, wills, ordnance survey maps, books, newspapers and more going back centuries. If you can't find record of an Oxfordshire ancestor online, it's certainly worth a visit, and the helpful staff are happy to answer queries on how to best go about finding what you're looking for.
On a related note, we would also like to help you answer the more immediate question of "Where Have They Gone?". If you have a friend or relative you can no longer locate (and you can't find them on Facebook or Friends Reunited), visit Missing People (formerly The National Missing Persons Helpline). You can post details and photos of those missing and look at the age progression section to picture how someone from the past might look today.
Good luck!