At the start of each session a ballot is held - and the lucky backbenchers who are chosen get the opportunity to introduce a bill of their choice. Further details of PMBs can be found at http://www.parliament.uk/DOCUMENTS/UPLOAD/L02.PDF
The ballot is not the only way for a member to gain an opportunity to introduce proposed legislation. The 'Ten Minute Rule Bill' procedure gives an MP a prime time spot to ask for leave to introduce a bill - though this is often used to publicise an issue rather than to bring in legislation. MPs can also present a bill, but no time is given for further stages.