First, make sure the new version of DuetWebControl is compatible with your firmware version. For this example, we'll update the DuetWebControl 1.07 that comes with the latest dc42-r firmware to the new DuetWebControl 1.08.
DuetWebControl is found in the /www folder on the compact flash card with your other Duet configuration files. The first thing you need to do is download the new version of DuetWebControl from GitHub at the link above. Click the Download Zip button. Rename the downloaded folder to www.
Next, insert the Duet's flash card in your computer's card reader. Find the www folder and rename it. I like to use the version number in the new name, so for this example I'd rename to www-107 to reflect the 1.07 version. Now copy the newly downloaded www folder to the flash card. When the copy is complete, you can eject the card and reinsert it into Duet and restart.
To check that you have successfully completed the update (or just to check the current version) open the DuetWebControl in your browser. Click the Settings menu on the left side of the screen and make sure the General tab is selected. The current RepRapFirmware and DuetWebControl versions are displayed as shown here.