I am interested in tracing my family name [Leith] But I have no idea where to start. I would prefer it if it was free as well. I tried local libraries but they don't do the records. Only books. Any suggestions?
You need to find your local Public Records Office to access birth, marriage, death, etc. records. It's free but you will probably need to make an appointment. Their website also has some useful information for those beginning to search their family history - http://www.pro.gov.uk/research/familyhistory.htm
Another good place to start is http://www.familysearch.org/
they give excellent tips for beginners. Good luck with the search if you need more help then just come back and post a new question .. that way it won't get missed.
There are plenty of free Internet resources to help in your search, and some very kind people who will search small bits (eg census look-ups) free as long as you're nice to them. Look for them at http://www.ukgenealogy.co.uk/index.html
In addition, http://www.rootsweb.com
is an immense site full of info on how to get started, searchable databases etc etc, and also has mailing lists by surname and county so you can ask the most likely people for information.