I'll make a deal with you... I'll tell you EXACTLY when to book to get the lowest fare, if you'll tell me what the winning lottery numbers will be.
There is no definitive time to book (ie: 4 weeks before the trip, 6 weeks before, 3 months, etc). As far as when you should book... when you see a price that's acceptable to you. If you book through an airline that doesn't allow credits if the price drop, don't look at prices again.
Now, someone will come on here and say they always get the best rates at 6 weeks (or 4 weeks, or 2 months, or whatever) before the trip. The last couple flights we've taken as a family (Orlando, Mexico), we've booked within a couple weeks of when the flights were announced (Delta, so ~300 days), and the prices never got lower.
I'm sure this isn't the answer you're looking for, but it's the truth.