From long experience, I have some advice. September is usually a great month for standby's, as is October. Fly after Labor Day....at least a couple of days. Monday mornings are bad, as are most Sunday and Friday flights. Tuesday, Wednesday, Thursday and Saturday flights are usually pretty good. Also, flights that leave VERY early are usually wide open. I used to fly Northwset standby out of ATL all the time. I would usually hit the 6:30am flight out of here and take my chances in my connecting city. Another reason for very early departure is that you'll get to your connecting city and be available for most or all of the connecting flights on that day.
The Delta employee who got you this pass may be able to look in the computer and see how flights look.....open or oversold. My Dad did that for me. I usually had a printout of the standby list, which included seating priority, so I knew when I'd be called and what to expect. The bad thing about that is that you can only get a good idea about a week or so before the flight. Of course, you can see way ahead of time if the flight is packed, but you get the best perspective a week before. The bad thing about that is getting time off from work or having an employer who can be flexible with vacation days.
Other tips.....

If you have to dress up and you may be looking at a long layover in your connecting city, bring a pair of comfy shoes to put on til it's time to try the next flight. Beware of the gate agents though. They do check your attire. Another good tip is to pack extra clothes and undies and basic toiletries in your carry-on. It's happened to me many times before that my bag would make the flight, but I'd have to wait. If you get stuck in an airport for long hours, you'll be glad. It's also great if you get stuck overnight. Been there, done that....no T-shirt though...
I wish you luck and will answer any more questions, if you have them. Have a great trip!