You start by talking to all your surviving family and gathering every bit of information they can provide before they pop their clogs.
After that you subscribe to a site or use freebmd to check the records of those you know and find out who they may be related to. Use census too when they allow you to see them.
You purchase birth marriage and death certificates to get more info.
And if you need more you go around the country looking at graveyards and reading parish records. Also joining a local genealogy club or taking a look in your nearest town library may help too.
Get yourself some decent software to record al the information you get.