Dave, thanks for sharing this Delta page! It gives me so many travel ideas for this winter.
There have already been lots of great tips - traveling in the shoulder or off seasons, being flexible with destinations and dates, searching aggregate sites. Using these strategies, I've booked good airfare to Europe about a month out.
I also recommend downloading airline apps. I have American, Delta, United, and Southwest on my phone. When they have sales, I get push notifications. Southwest has them quite regularly. (Last year, my husband and I flew roundtrip to New Orleans for just $89 per person!) In September, American had European flights on sale.
If you see a fligth deal, don't wait to book it. Websites love to change prices quickly. You have 24 hours after booking a flight to cancel, so you have time to change your mind and get a full refund.
Another option is bundling your trip. In the US, we use Expedia. For European travel, we prefer Trip Masters. By bundling your hotel(s) with your flights, you can save some extra money. (However, watch out for non-refundable hotel rooms, which can complicate cancellations.) Before booking, we price out the packages by looking directly at the hotel and airline websites. A couple years ago, we saved $1,000 on a week long trip to Lisbon and Porto by bundling the hotels and flights.