Genuki: UK &Ireland Genealogy (www.genuki.org.uk). 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 Public Record Office (www.pro.gov.uk/research/familyhistory.htm), which will help in the use of documents pertaining to births, marriages and deaths. This in turn is linked to www.familyrecords.gov.uk, which has records from Ireland and India.
Or you might wish to try Cyndi's List, as 18 million visitors have done before you. A massive 85,000 links constitute Cyndi Howells' personal attempt to organise on-line resources on genealogy. Visit www.cyndislist.com.
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. In which case The Commonwealth War Graves Commission are the people to whom to turn. Records of 2 million graves from both world wars and details of 60,000 civilians who died in the second world war are available from www.cwgc.org.
www.familia.org.uk is where you'll find a guide to the public library's genealogical resources in both Britain and Ireland. You can find what electoral records, census data or past newspapers are available in your local library.
Other related sites include www.genealogy.com, www.ancestry.com, www.familysearch.com, www.origins.net, www.sog.org.uk, and www.college-of-arms.gov.uk The first three of these have somewhat of an American bias and some may charge for their services.
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, visit www.missingpersons.org, the online home of 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.