Airfare

Check once a month, pull the trigger when you can live with it--but certainly before three months out.
Become familiar with the options for your route and which airlines to keep an eye on.

Use Google Flights and set up some Price Alerts

Purchase when you see a price you like then don’t look back
Always book with the actual airline

I usually purchase in the 5-7 month time frame

Good time for the best airfare price?
Like others have said you will need to establish a baseline of a price then go from there to determine when you see a "deal". For me that deal would include a late departure (like 4PM) so I don't have to spend more money on an overnight Hotel for a morning departure (We drive to 2 hours to get to LAX and one accident can mean we miss the flight), a non-stop flight or if we have a connection at least a 3 hour layover and a decent arrival time to alleviate jet lag (Find lodging, get dinner, walk around, to bed by 10PM). I hear stories of people who arrive at 6AM, have an airbnb that won't let them check in till 2 and have to walk around with luggage, did not really think that one through.
You can set up google flight for notices and also subscribe to scotts cheap flights emails (free) which will email you all kinds of deals that usually last only a few hours or days. Scott's is how I found my last two deals on Europe Airfares on airlines I would never have considered and they all turned out great.

Buy when you can stomach the price. There are no guarantees!

I basically take Letizia's approach. Fares can move up and down a lot from one day to the next; I once watched my planned itinerary bounce between $800+ and $1300+, over and over again. My goal is to avoid buying on one of the fare increases. That means I try to check fares daily once I've decided on my destination and travel date.

Setup alerts on Google Flights for sure, but buy the ticket directly from the airline. Google doesn't provide as much info about what you're getting, and without a middleman you'll have more recourse in case of of something outlandish happening like a worldwide pandemic. Some studies have suggested 5 to 6 months ahead is the best time to buy, but averages mean little when there are so many variables.

We booked airfare in mid-September for our trip that starts in mid June to early July. We are flying from San Francisco to Rome and then back home from Milan. We have a stop in Montreal both ways. Since I booked our trip prices have gone up so I’m happy.

We are planning a trip to France and Belgium for September/October 2023. Prices for the airline we like to use are very reasonable right now, so we think we will purchase. It’s the proverbial crap shoot for fares and best time to buy.

We already bought our tickets for flying from Denver to Portugal next June. I agree with the wise poster above who said -- once you buy your tickets don't look back.

There always used to be some rules of thumb about when to buy tickets, but it seems like since COVID there aren't any patterns any more. And with so many people traveling, there's no reason for the airline to offer cheap fares. Every flight we were on this past summer was fully loaded.