Start by finding out everything you can from living relatives; dates of birth, marriages, maiden names etc. Hopefully you should find out enough to locate great grandparents on the 1911 census and from there work back through the previous censuses.
Both Ancestry and find my past offer free trials and the Mormon site Family search is free and I've found it useful for pre-1837 records.
If the family you are researching were local to where you live, you'll probably find lots of info at your local library or records office, for example, parish records of marriages and baptisms.
If you need to order birth, death or marriage certificates, use the freeBMD website to search, make a note of the registration details and then order from the GRO website. Still costs around £10 but much cheaper than ordering through ancestry.
Try googling unusual names or putting them into newspaper archive searches, you may find some interesting stories or find other people researching the same family.
Rootschat is a very helpful forum and they have plenty of info for beginners.
That's about all I can think of at the moment. Good luck with your searching and beware, it's addictive once you get started!!!