The best way to find cheap airfare is through Airfarewatchdog.com. All they do is list airfares so you will not be able to book through this site. You will have to use Orbitz. On AFWD you can search from a city or to a city. Both functions work really well. All prices displayed include all taxes and fees, i.e. out the door.
You can also sign up for their RSS feed and customize what you are going to see. They also have a twitter feed you can follow. Some of the flights are only there for literally just hours. I live in Salt Lake City and I booked a flight to Lima, Peru (hello Machu Picchu) for $248 r/t. When I checked a couple of hours later, they were gone. There was also one to Cancun for $198 for Christmas travel. My wife was in the mountains for a couple of days and out of cell coverage. I knew she was leery about Mexico so I didn't book without speaking to her. The next day, they were gone. So sometimes you have to move fast.
Its really great in that you can travel to a lot of places that perhaps you wouldn't normally think of going-a little off the beaten path. Some sample fares that I have seen from SLC
$432 to Dublin
$500 to Istanbul
$550 to Moscow
$650 to Johannesburg
If you don't see a city, AWD does not consider it a deal and won't post it. The top 50 fares are what they consider to be their best deals on that day.
Do not fly Spirit Air. I cannot recommend them at all. Do some research online and you will see why.
Another way to search is through Hotwire and their flexible date search.
http://www.hotwire.com/air/flex/index.jsp?You can search any 30 day window here. Again, all flights displayed are with taxes and fees. If you are leery about booking with Hotwire (I am not) usually you can book these flights directly with the airline. This matrix is a great way to find the best prices.
Probably more thn you wanted to know, but you can find some amazing deals. We flew from SLC to Hawaii last December and spent Xmas in Hawaii. Christmas morning was spent on the beach-my kids loved it! Our tickets were about 330 a person in the highest of high times to one of the most desired destinations in America.
Good luck and happy searching.
Edit: Thanks to BearyWhite for noticing my original Orbitz link was not working. Orbitz has slowly been removing this feature from their website. It used to be right on the main search page for airfares. They then buried it on their site making it hard to find. It looks like they removed the link completely on 02.12.13. I have replaced the old Orbitz link with Hotwire. Both serve the same function.