The remote is pretty simple to take apart.

There is a screw (I don't know what these are called in English) underneath one of the rubber cushions on the back of the remote. If you put the remote on the table, with the screen facing down, so you can read the label. The screw is under the top right rubber cushion.
Then there is four more screws underneath the label.

Once you have removed all of these you should be able to remove the cover without any problems.

For those in Sweden, you can buy a new battery from www.hembiobutiken.se by sending an e-mail to them. A new battery is 590 SEK.