Theres no need to go into travel agents or call airlines to book flights anymore. Rather than waiting for them to do all the searching you do it all yourself when it suits you. There are a large number of cheap flight sites around but often it is better to go direct to the cheap airlines sites themselves where the prices (before they add tax!) are often ridiculously low.
You can see the arrivals screens in the airports on your PC. For smaller airports the information is on the BBC website. Simply enter the relevant city in the BBC page, & then follow links for Travel.