How can I find the cheapest time to fly between two given points?

I found it depends. Sometimes one website gave me a better option for long haul flights (expedia) while others were better for shorter.

I would chose 3 or 4 websites that cover the main airlines which fly from your airport and follow then every few days (I used to look at the them everyday if I was searching for a particular deal) for the dates you are travelling. I got used to the cost of the flights and sometimes playing with the dates by even a few days made quite a difference. When a deal/special etc came up, I then could tell if it was better than normal or a great deal.

So get to know a few websites and make them your friends. I used to look at them at the beginning of the day or every evening. It only takes a few minutes.

This is almost impossible now that most airlines use the pricing model of adjusting fares from day to day according to demand. What is true today might not be true tomorrow.

Prices tend to go down with time to get the seats filled, then up again as the date approaches to catch people who have to fly at short notice. What I tend to find mostly works is booking 2-3 months in advance hits the cheapest time. At really popular times that might not work but in general it seems to.

I like to use KAYAK http://www.kayak.com/ it has been pretty effective for me. They'll show you a range of days that are cheap and if you stay on top of things you can plan ahead for a cheaper day/time or sometimes even get a last minute good deal!

Enjoy your travels! :)

Kayak is the best place to look at a range of dates and the various flight options that are available.