Where to Book Flights

Where to look, and where to book are 2 different questions. Look on a search site like Google flights, Skyscanner, Kayak, etc. They will show the available flights and prices for your dates. Then go to the airline website to make your booking. Deal directly, not through some 3rd party site which will only complicate things if a problem arises.

This recent thread on prices for flights might be useful. https://community.ricksteves.com/travel-forum/transportation/airfares-dropping-for-the-time-being

I always start with Google flights, as that will show me most major airlines and prices. Plus Google does not book the flights - it sends you to the airline. https://www.google.com/travel/flights

When you go there, decide if you want to look at one-way fares, round-trip fares, or multi-city (fly into one city and out of another). Add your information, and it will spit out flights for you to look at. Click on one you like, it will show you the return option (if you picked RT and MC) and once you've clicked on the return option you want, it will take you to the airline's website for booking. You also have the option to have Google track the prices so if a lower price appears, it will send you an email.

Use skyscanner, google flights, kayak, etc for research. Booking direct from the airline is the best way. However, sometimes, an OTA like Expedia may provide a flight option which is not available on the airline or much cheaper than the airline. For example, we bought open jaw tickets for Portugal which used a combination of flights with British Air and Iberia. We could not book the same combination on the airline website. I could have booked the combination by telephone directly with the airline, but the cost was several hundred dollars more per person. So, I used Expedia.