I'll create a help guide for this with pictures when I have time. Short version: go to Account Settings > Notification Settings > Mentions & My Content (click downward carrot on right to expand). Select your desired notification options. Notification List is the little bell icon at the top right of the forum. Email is...well, I think that one is axiomatic I suggest checking this for the remaining categories to make sure you receive notifications as you wish. We don't (yet?) have a Newsletter or Events, but might as well set those correctly in case they are added in the future.
At the bottom left of the Notification Settings page, select if you want a browser notification and/or your device to play a sound when you have a notification through the Notification List. On the bottom right, confirm you have entered the correct email address. Also make sure to check your junk folder for notification emails.
Although I have set notifications at a global level, I suspect some individual user settings came over from the old forum and are overriding them for some of us.
-John