For the initial set up of Electrum with BitBox02 please refer to our introductory blog post on the matter: Use the BitBox02 with Electrum wallet Part I.
Once you have successfully paired Electrum with the BitBoxApp you can proceed with the following steps to sign messages.
1. Click the section 'Addresses'.
2. Select the address you wish to prove ownership of within the displayed list of addresses and use a right-click to see a menu.
3. Click 'Sign/verify message'.
4. Copy and paste the message you need to sign [1] and click the 'Sign' button thereafter [2].
5. Proceed to sign and double check entries on your BitBox02 display as seen in the following video: BitBox02 sign message with Electrum.
6. Copy and paste the generated signature to where you need it.
Voilà! You've successfully signed a message with your BitBox02.