If you don't have any particular airline company in mind, the best you can do is to check one of those websites that search the best options for you through all the companies. I will give you a few of them that I have used many times. I have tried all the following companies and I never had a problem with them (these are not airlines, they act only as an agency. If there is any problem with the flight, then that's responsibility of the airline).
Orbitz.com - I use this one when I want to fly from the US. I found really cool offers and it's really easy to search.
Rumbo.es - This is actually a Spanish one, but I have used it for many international flights. It's the one I use the most, because it usually gives me good offers to fly to and from Spain. However, it's worth a shot!
Edreams.com - That's very similar to Orbitz.com, I usually check these three and then compare prices.
Another option is to book the flight directly from the airline company, which I have done sometimes. It's more difficult to compare prices, since you would need to check all airlines. However, if you have any particular airline in mind you would like to fly with, then I recommend you to check the website directly. I did that with Swiss Air, because I found some offers in the Internet, and Delta Airlines, because they had direct flights to Barcelona.
There are other aspects you should care about when looking for a flight. Specially when it's a long one, for example Europe - America. I always try to have as less transfers as possible. If there is no direct flight, you will have to change planes in a different country. However, to change planes you will need to board again, which means you will need a lot of extra time. I try to have only one transfer, if direct flight is not possible, and I try to have a short transfer. I had to wait 10 hours in Germany waiting for my next flight, and that was something I don't want to repeat! I would say 1:30 hours up to 2 hours is perfect. I wouldn't take a flight with less than 1 hours for the transfer, because it might be too short and you might lose your connecting flight!
I hope the information was useful and let me know if you have any questions! See you soon!