A "company" cannot become "Limited". A company IS "limited". That's what it means "Limited Company". The only companies that are not "Limited" are those that are even bigger "plc's".
If you meant how does a trading partnership or sole trader become limited then it's just a matter of incorporating by setting up a limited company (companies such as Oswalds will do that for you) at a cost of �250 or so and starting to trade from that instead. You need to inform HMRC obviously and it would be best to get an accountant to do it for you but it's not difficult.
The thing that most people struggle to get their heads round if they incorporate their business is that money and assets of the business then do not belong to them. It's company money and whilst you may be the only shareholder you can't just help yourself to funds. There are tax implications of doing so.