First find the latest update file for your device in https://redmine.replicant.us/projects/replicant/wiki/ReplicantImages, it will look like that:
replicant-6.0-<yourdevice>.zip
1. Make sure the device is connected to the Internet
2. Navigate to https://redmine.replicant.us/projects/replicant/wiki/ReplicantImages with a web browser
3. Download the update file
4. When it finished, check in the "Download" application if everything went fine. If it didn't it will show some error message.
1. Press the power button
2. Select Reboot
3. Select Recovery
4. Press OK
1. Select Apply update
2. Select Choose from emulated
3. Select the update file, which looks like that: replicant-6.0-<yourdevice>.zip
The file will usually be located in 0/Download, so select 0, then Download, then the file.
4. Confirm the installation
5. Press the back key (if necessary) to get back to the general menu
6. Select Reboot system now to reboot the device
7. Your device should now be updated!