The search for our Italian relations should start with exactly the same sources you would use for searching for anyone who lived or died in Britain. The Anglo-Italian Family History has produced a useful pamphlet Tracing your Italian Ancestors that you can download or view (depending on your browser settings) that details the various Italian sources of information. If you are a complete newcomer to family history, try the following introductory sites:
Start with the documents already in the family: certificates of births, deaths, marriages, memorial cards, family bibles, photographs, military records and medals, passports, letters etc.
Interview older friends and relations. Even if they claim not to know much, by chatting around a subject and asking questions you may find they know more than they think. Record every clue, but take everything you're told with a pinch of salt!
When you've built up a picture of what you already know, it's time to start searching the British civil records for records of births, marriages and deaths that occurred after the family arrived in Britain.
The Links page gives a wealth of information for researching our Italian ancestors in the UK and Italy.