Sometimes fares which involve a connection are cheaper than direct flights. So if all the fares are non-stop, ask if flights that involve a connection are cheaper. For example, flights from Pittsburgh to Boston on TWA are often cheaper than flights on Us Air, because Us Air offers non-stop service while TWA flights are routed through their JFK hub.
If all the fares are on one airline, ask your travel agent if there are cheaper fares on other airlines. Be prepared to ask for specific airlines. Don’t run down a list of a dozen airlines but ask for two or three. If all show similar lowest fares, you aren’t likely to do better on another airline. (Obviously, this advice doesn’t apply if you^re calling the airlines directly. If so, call 2-3 airlines before purchasing tickets.)
If there are two airports near where you live (e.g., Washington DC, New York), ask if fares from the other airport are cheaper. It may pay to drive 40 miles to save $100 on airfare.
If you qualify for special discounts (youth, student, senior citizen, group traveler, etc.) ask about the availability of such discounts. If you don’t ask, they won’t volunteer the information — how are they to know whether you qualify?
Tickets are generally cheapest for travel in late August and from March (excluding Spring Break) through mid-June, when air traffic is the lowest. Of course, this rule of thumb depends a lot on the destination, since some destinations have strong traffic year-round.