For those who don't know how a Non-Realtime Tourney works (A video is available with more detail):
As soon as the Tourney is active, go to the Tournament Page by selecting Profile, Events Tab, and click on the tournament. You will see the Tournament Page with a blinking icon indicating you have a match waiting to be scheduled. Hit that. This will open the Scheduler. (Note: if there is no Scheduler button, you either have a bye or awaiting another match to be completed before yours is generated.)
You can then propose a date/time to your opponent. The opponent will receive a Message with the proposal where he or she can Confirm. Note the Scheduler icon will always be available during the Tournament if a date/time proposal is waiting. On winner side, you have X days (where X is specified on the tournament page) to schedule the match and play it. Loser side: half winner side days. If you both accepted a date/time but you both want to re-schedule, ask an Admin to clear the Scheduler for that match. This can only be done -before- match deadline.
If the opponent can't play on your proposed date/time, he or she can counter-propose. Again, you will then receive a Message with the counter-proposal and the Scheduler icon will be blinking on the Tournament Page. If you agree on a proposed date/time, hit the Confirm Button on the Scheduler.
All scheduling operations send Messages (see Message on nav bar) back and forth between you and your opponent. You also get emails if enabled in your Profile. There are links for scheduling in these messages making it easy to accept or counter propose dates.
When the match is confirmed a date/time shows up in the tournament bracket.