rule of thumb would be the sooner the cheaper, but how many weeks or months in advance?
For my particular flight there are only three companies and it seems flights are cheaper between Tuesdays and Thursdays. However, if you want to book a flight 2 months from now, it’s considerably cheaper.
Have you found the sweet spot?
Hopper is an app that can show you when the best price is, and can recommend for you when to book your fight or give you alerts when the price drops. 3 weeks as others have recommended is generally an excellent sweet spot but it can also help give you a little more analysis. I highly recommend using it for that.
DO NOT under any circumstances actually book with them. They play elaborate games with the pricing (up to and including offering you coupons good for cash discounts on artificially-price-increased tickets so your discount works out to exactly $0), they add extra stuff to charge you for (including a $5 “tip”) which the boxes for are checked by default. Booking with any third party as opposed to directly with the airline reduces some key benefits you’d otherwise get such as cancelling for free within 24 hours, which has screwed me before. Overall I’m sympathetic to their struggle to run a business which provides a service to people which gets them $0 revenue, and bravely trying to make it work anyway, but the way they do it is solidly customer-hostile.
Their features of watching the price and telling you when to book, last I checked, still work perfectly well and are excellent, though, and free if you never book with them.