Start with the free sites already mentioned and also by talking to living relatives. Write absolutely everything down and verify everything - people often get things muddled up, forget or just downright lie!
If you're really serious though, you'll have to spend some money, although it needn't be masses. Never believe anything you see on the Internet without getting the evidence yourself - I know loads of people who say that after spending a couple of hours on the Internet they've gone back several generations and got hundreds of names on their family tree. I just wonder whose tree they're tapping into, probably the wrong one!
Work backwards - for example get your father's birth certificate and use the info on that to find his parents, getting their birth, marriage and death certificates if you can, they are only £7 each. This is the slow way, but the only credible way.
You can use public libraries to search the BMD indexes for free, or use www.freebmd.org.uk, but again use this as a starting point and check the index yourself before ordering the certificate.
Use census material - if your ancestors were local you will be able to do this for free at your local library or local studies centre. Otherwise, you can search on the Internet on a pay-per-view basis, or buy census CDs.
Use sites like www.genesreunited.co.uk - I have found several relatives this way, but also many false leads, so again be wary.
The Internet is a great tool, but sometimes you have to do the leg-work yourself too, and often it's more exciting that way. The thrill of getting a certificate in the post and finding a new bit of information is priceless.