I tend to fly cheaply with multiple transfers/layovers. What I figured out recently is that it is nice to combine the flights in such a way that one of the layovers is _longer_.

When the airport has a good connection to a major city then 12 hours during the day are enough, but I'm happy to bump it to 2-3 days.

I have managed to visit some Chinese and Canadian cities this way and it was both more interesting and much cheaper than taking a direct flight.