It's usually very easy to remove this coding but 'official' sources (e.g. retailers or manufacturers websites) won't tell you how to do it. (It normally involves something as simple as opening the disc drawer and keying in a short number via the handset). So, unless you bought your DVD player from someone who 'broke the rules' by removing the code prior to purchase, you'll have to use a 'hack' to remove the region coding yourself.
To search for the relevant hack for your DVD player, try here:
http://www.dvd365.net/?hacks/hacklist.htm
If your player is not listed, Google the make and model of your player together with 'multi-region'.
If you're still confused, you could always consider buying a new DVD player from Richer Sounds. They've got branches in many parts of the country (and they sell online). Unlike most other retailers, they sell multi-region players. (This usually just means that the details of the 'hack' are stuck to the side of the box). Their cheapest multi-region model is �19.95:
http://www.richersounds.co.uk/showproduct.php? cda=showproduct&pid=ELTA-DVD150
(However, you'd have to check whether it's in stock at your nearest store. It's currently out of stock online).
Chris