This BBC guide explains how to research your ancestry: http://www.bbc.co.uk/familyhistory/ The following free forum is also useful for asking more experienced genealogists questions and looking up lists of local resources: www.rootschat.com
Basically, you start with yourself (and possibly any siblings) and work backwards, generation by generation. For each person you research, try to find out at least the following details:
Their full name
The date and place they were born and/or baptised
If they were married, date and place of marriage and full name of spouse
If deceased, date and place they died and/or were buried
Most crucially, their parents' names, so you can trace back another generation
It may also be both useful and interesting to find out other details, like what job(s) they did (this can be essential for elimination purposes if you find two people with the same name in the records - if you know your ancestor was a fishmonger, it can help you to identify which of the two people is your ancestor and which is just some guy with the same name)
How do you find out this information? When dealing with living relatives, the best way is by asking them! If your mother tells you she was born on e.g. 1st May 1944 in Ealing, you can probably trust she is telling the truth without needing to see any documentary evidence. However, you should be careful about trusting what your relatives say about other relatives - sometimes people make mistakes, so it's always best to check records if you've heard stuff secondhand.
Other ways of finding out information about relatives include:
- any private family documents, like diaries, family bibles, things written on the back of old photos etc Ask all your relatives if you can see any family documents they have
- ordering birth, marriage and death certificates (although these are expensive. I know I'm going to be thumbed down by the entire world for saying this, but I only order them as a last resort, if there is no cheaper method of finding the same evidence. The great advantage of bmd certificates, though, is that in theory, at least, they are a complete resource - if someone was born in England between 1837 and today, they should be on there
- searching for birth, marriage and death announcements or news articles about weddings and funerals in local newspapers. The British Newspaper Library has a great site, although you have to pay to read articles http://www.britishnewspaperarchive.co.uk/
- information on tombstones (sometimes called monumental inscriptions or MIs in the genealogy world).
- census records. Unfortunately, you have to get back as far as 1911 for these to be any use, as they are only released to the public after 100 years. Parts of the earlier censuses are available on free sites like www.freecen.org.uk and (if by any chance you're Cornish) the brilliant Cornwall Online census project http://freepages.genealogy.rootsweb.ancestry.com/~kayhin/cocp.html, but you can get a complete set of censuses on paid sites like Ancestry.co.uk (you can use it for free in many public libraries) or findmypast.co.uk. These are a great way of finding out who your ancestor's parents are - if you know he/she was born in a certain village around 1865, if the only person of the right name in that village in the 1871 census is a 6-year-old child, living with his parents John and Mary, then you've almost certainly found the right family.
-local parish records of baptisms, marriages and burials. These are most useful once you get back before national bmd registration. www.familysearch.org has a searchable database of transcriptions of parish records, but it (a) does contain inaccuracies (b) isn't complete - some parishes weren't included, so just because you only find one John Fothering-Smythe born in 1775 on FamilySearch doesn't necessarily mean he was the only John Fothering-Smythe born in England in 1775. If you know where your family came from, online parish clerks schemes (where local volunteers offer to look up and e-mail information to people who can't travel to where the records are) can also be very useful http://www.genuki.org.uk/indexes/OPC.html
While Clive, Maxi etc are right that you can only completely trust real records, not transcriptions or indexes, I think it's fine to work from transcriptions and indexes when you're starting out, especially if you're only doing it for fun, not publication - you can always check against the real records at a later date. You will probably make mistakes to start with, but the learning curve is part of the fun and I'd hate to put anyone off trying this fascinating hobby by giving them the impression that you have to buy lots of expensive documents right off.