It depends on which route and class you want and which airline you are redeeming for, and how flexible are you with your schedule.
For some really popular route such as SYD/MEL/BNE-LAX on QF first or business, you pretty much have to book 12 months in advance. This is a very popular route and QF only release a few award seats so by about 11 months out, it almost disappeared completely. On VA, it used to be quite easy to redeem but recently that has changed.
It you are just looking at domestic redemption in economy, you can probably book anytime, as there are so many flights in a day so lots of award seats.
If you are very flexible (eg. Retired couple who can practically just pack and go), many airlines do release seats on the last 2 weeks prior to departure (eg. Cathay and Lufthansa) as they have a lot more idea how many spare seats they have. So you can book just 2 weeks out and usually availability can be pretty good.
It also depend on which airlines. Thai, Asiana and ANA are known to be consistent and generous. So unless in peak seasons, you can still find seats at a few months out although it may not be on the day you want so you have to be flexible.
The worst time though, is about 3-10 months out. During this time, most award seats that were released initially have already been taken, and airlines usually don’t release anymore seats during this time as they will try to sell them. Most people also have their holiday planned during this time so award seats tend to be very competitive.
Personally, due to my work I am not flexible at all so I must travel on a certain date. So I tend to book at 11-12 months out and I can always find award seats on the day I need to travel (of course that is across different airlines from different alliances on different FFPs). The beauty of award booking is that all tickets are refundable (with a small fee). If my plan changes somehow, I can easily get my tickets refunded.
Because award booking is an ever changing thing. An airline that is considered generous today may change any time (eg. EVA which was very generous on the first year when they joined star alliance has suddenly without warning shut down many long haul award spaces. VA might be doing the same as it’s award availability suddenly vanished. Etihad and Air China seem to come in waves. Some months they can be generous and some months they can be stingy!) Award charts also changes (devalues most of the time). So my advice is, if you see one award that suits you, grab it as soon as u see it. Just cancel it later if your plan changes.