Tracing a family tree
There are thousands of webpages of advice for tracing a family tree. For Great Britain, Genuki is a good place to start.
For the UK I would also recommend http://www.ancestry.co.uk/ , as frequently seen on the BBC series "Who do you think you are". They do charge a subscription fee, but they have all the UK census information from 1841 to 1911 ( can search using indexes but there are a few errors in this, you need to be inventive trying to get round the copying mistakes).
Indexes to England and Wales birth marriage and death certificates can be found at http://www.freebmd.org.uk/ . For a marriage, you can find out for free who the person married by clicking the page number, it shows the spouse who is listed on the same page. Otherwise you would need to then order the certificate to get the information you need ( parent's details etc). These can be ordered from ancestry.co.uk , or the General Registry office http://www.gro.gov.uk/gro/content/certificates/ . For Scottish records, the official site is Official government source for Scottish genealogy, census and family research - ScotlandsPeople
If you can get back to 1837, the Mormons (Seventh day adventists) have copied and catalogued church birth and marriage records, which can be searched on the web for free here http://www.familysearch.org/Eng/Search/frameset_search.asp (the IGI index). However, there are many mistakes in these entries, it is always best to go to the original source if possible. These church records, in England anyway, only go up to about 1837, when births, marriages and deaths had to be registered. It gets harder to trace families later, particularly since censuses are only released after 100 years, and people tended to move around more towards recent times.
Better than all the official records though, is your own family. Contact all the relations you know, and ask them to contact all the relations they know, to see what they can add to your records. After all, you may not at the moment know all your second cousins, but they may have some useful family heirlooms of your common great-grandparents.
It may be a family tree written in a bible, or family photos, or even just memories of your ancestors' lives. These human-interest aspects cannot be found in official records, (unless possibly they were mentioned in a newspaper). Your relations can hopefully get you back to a time when official records are more useful.
There is no need to rush into searching through official records, they will not go away, and in fact it gets easier with time, as more data is put onto the web, and censuses are released after 100 years.
But if you think you might like to trace your family tree one day, it is vital to starting asking your relations NOW. Memories fade with time, and sadly eventually elderly relatives will die. It would be a lasting tribute to them if you have recorded all their family stories, perhaps even videoed interviews to keep for the future.
Good luck !