If you're flying somewhere that involves a transfer, say from Canada to Australia which typically involves Canada to LA, then LA to Australia, consider that it may be cheaper to book these two legs separately on your own by adding another destination to your trip. It should go without saying that in doing this, you should not book tight layovers. I repeat: do not book layovers that are hours apart! This approach is for those who want to create an additional destination of a few days or more, before catching their next flight. The one exception is when booking with Kiwi.com, who offer their own guarantee on making connecting flights even when not with the same partner airlines.
Keep your dates flexible. Many airlines have specific requirements for a minimum and maximum total number of days to be spent in a location in order to get the best deal. For the cheapest flights, stay for a minimum of 2 nights and a maximum of 30. Try to stay at your destination over a weekend, as flights that bookend a Saturday night are cheaper than those that lack a Saturday stay.
In Google Chrome or Safari, incognito is enabled by hitting Command (or “Control” if using PC), Shift, “N”. For Mozilla Firefox or Internet Explorer, hit Command (or “Control” if using a PC), Shift, “P”. This will open a new browser window where your information is not tracked, thus not inflating prices as you search. Note: if you're using an older version of OS X, open Safari then click “Safari” in the menu bar, and select “Private Browsing”.