I have just completed planning and purchasing airline tickets for a month long visit to multiple cities in the US.   Using the Internet to do so is a must and can be an exhausting process.  If you are looking for the best deals with cheapest prices, things have changed in recent years.   It used to be a quick visit to (Oribiz.com, Expedia.com, or Travelocity.com ) would be a great place to compare fares and find a good deal.   Then, over time I noticed that sometimes going direct to the actual airline website gave a better deal or other flights that were not advertised.    That made the process of getting the best deal a lot of work.

There have been many other websites that advertise "cheap tickets".    Visiting most of those is even more time consuming and rarely did I find better deals.

That all changed when I have discovered two websites that gave significantly different and better information when planning a trip with cheaper airfares.

The first one is called Sky Scanner.   
https://www.skyscanner.com/tips-and-inspiration/best-time-to-book-usa
Not only do they give great pricing deals, they have a tool that shows how many weeks in advance to book plus many tools to find the very best deal.   I used it extensively and was impressed with the volume and detail information available.  We planned many one-way hops and the prices varied greatly.   It is now my "go-to" website for getting airfare information, tho I often still book with the actual airline.

The second one is called  Skip Lagged
https://skiplagged.com/
This site has some useful information but is more aimed at a traveler that does not have and checked luggage.   Often times airlines will have flights that are multi-stop and are cheaper than direct flights to one of the layover points.   I never understood why flying further was less expensive - can't we just pay by the air mile?   

For example, say you wanted to fly from Atlanta to Denver.    The airfare for that direct flight might be more expensive than a flight that goes from Atlanta to Portland, with a layover in Denver.    So you could purchase the longer flight to Portland but you would not board the plane for the second leg from Denver to Portland, thereby getting to Denver on a cheaper airfare.    This would not work if you had checked luggage since your luggage would go all the way to Portland.   On the other hand it provides a useful option for some people.  They also give a very interesting graph of airfare prices between now and when you plan to go, helping you see when the cheapest times are to fly.

So, if you are planning a flight, I would suggest checking out these two sites.    Then book direct with the airline or take the information to your favorite travel agent.   I have easily saved almost $1,000 over our extensive trip.   I only wish I had learned of these tools earlier.