You first gather information. Speak to relatives before they die, prioritise elderly ones. Then join one of the genealogy websites to seek out data from BMD certificates and census forms. Meanwhile find a genealogy software you can work with.
You can get an older version of Family Tree maker on Ebay for about £12 which will also give you 3 months access to Ancestry.co.uk.
Do not assume that all information you find is correct - check it carefully.
In the program always write names in the same way - and dates should be as 02 Mar 2016 or it will not search or catalogue properly.
My Heritage uk is the site I use diesel. Very good, log on and the site will take you through it. I cant post the link, it automatically takes me to my family tree. Haha. You will get enough for months of work and research from the free sources. When you need to go deeper there are costs involved. You can decline or choose what level of expense you are prepared to incur.
I have traced family right back through 7 generations to the early 1700s America, and Australia. My Heritage provides the facility to build a family tree.
Gather the D.O.B of every living relative before you start and have maiden names sorted where you can, Mothers and Grandmothers are very interesting.
Great fun, but addictive once you get going. Be prepared for some very strange revelations.
I have found it very useful over many years. There are many other websites available too. It's essential, however, to check records with other sources as there may be mistakes on line.