There's an ePub file linked at the end (where it says "Simply connect your Cybook or follow this procedure...", the word "procedure" is clickable). From that ePub:
Determining your software version- From Home, tap “Settings”, “About...”.
- The software version is displayed below “Boo Reader”.
- If “Version: 5.2 (build 1780)” (or earlier) is displayed, the Cybook is up-to-date.
- Otherwise, the Cybook can be updated automatically or manually, as described below.
Over-The-Air automated installation (via Wi-Fi)- Connect the Cybook to the Internet (by opening the ebook store or the browser). A dialog pops up to propose to install the firmware update. Validate to launch the installation. If [this update has previously been ignored, open the contextual menu (push the main button and tap “Menu”) and select “Check for update”.
- The firmware update is automatically downloaded then installed.
- The device restarts automatically with the new software version.
Manual installation (via microSD card)- Download the firmware update file from http://www.bookeen.com/en/supportdownload.
- Copy the file CybUpdate.bin onto a microSD card.
- Switch off your Cybook (Home, “Settings”, “Advanced”, “Shutdown”).
- Insert the microSD card.
- Press the main button (central button below the screen) and keep it pressed while switching on the Cybook.
- When the boot image appears (after about 2s), you can release the main button.
- Wait for a few minutes: The firmware update will start and, once completed, will restart the device automatically.