I want to travel to LA on points on a specific day in April 2016.

I want to travel to LA on points on a specific day in April 2016. When and how is best way / time to book?

Continuously since flight became available for booking and yet there is no guarantee. You have to be pretty flexible if you want utilize your points for classic award.

if you want to book a specific day on points you will basically need to book on the day that that day becomes available, if that makes sense.

So basically at the end of March start checking when the boking period goes out to and jump on it as soon as bookings open for the date in question.

As to how to book it, just on the QF website is easiest way

Yes, you need to check the QF site 2-3 times a day during March & April, for any award seats will go quickly.

Or get 40,000 United miles and book at your leisure.