Visit Account Preferences and select the "Enable push notifications" button.
Configure each notification type as desired.
Some devices may not support push notifications. However, first try installing the forums as an app on your device. This can be done through your browser. On some, it may say "Add to Home Screen." Once viewing the Account Preferences through the installed app, the "Enable push notifications" button will likely be usable.
Some devices may require the user to periodically have to re-enable push notifications by following these steps.