For flights I check multiple comparison sites for the best price. These are two of my favourites.
If you can be flexible with dates, check different dates and times to and from your destination and you can save a significant amount of money.
Be realistic about the number of flight connections and/or layover time you’re prepared to take. If you have an overnight layover you may find the airport vendors shut down and you’ll need overnight accommodation, which could wipe out any saving you make on a cheaper, less convenient flight. It’s not fun rocking up in a new location exhausted and needing to sleep for 12 hours, just to wake up in the middle of the night when you can’t go anywhere or do anything. Think it through.
Also join any airline reward programs you can. Even if you don’t fly often, loyalty points can often be transferred to other airlines in an umbrella program, and they do add up over the years. Several times my miles have expired so I’m more aware now of what airmiles I have and when they expire, so I use them when I can. With Airbnb, a free flight can mean that spending a weekend in a new location costs little more than staying at home for the weekend.