1) I always check the major travel websites first, to see what's out there and what the going rate is. These sites will quote the lowest available fare that they know of on the web. Great sites to start with are: http://www.orbitz.com/ and http://www.travelocity.com/.
2) If you prefer a certain airline or know that an airline services the area you are going to, check that airlines website yourself. Practically every airline I know of offers "internet only specials" that you can easily find by going to their web page. Southwest Airlines frequently offers internet only specials of only $39 each way to various places across the country. These may not show up on the sites listed in tip #1.
3) It helps to fly out of a larger airport than a smaller one if you want to save money. For instance, try LAX for cheaper flights instead of John Wayne (Orange County) or Long Beach.
4) Flying on "off" days are also cheaper. For instance, Tuesday or Wednesday instead of a Friday or a weekend. On the travel sites listed in #1, you can also enter in different dates and times to see which would be cheaper options.
4) You can always try sites like http://www.cheaptickets.com/ or http://www.priceline.com/ if you want a really low ticket price. Just be aware that any discount tickets do not allow changes or refunds.
5) If you want to buy a very cheap ticket but need the assurance that you could get your money back should something happen, you may want to look into getting travel insurance which might only be about $30 a person, versus an expensive plane ticket where you are allowed to make changes.
Overall, I would personally never buy from a travel agent, as they will not get you a rock bottom price, and they make money off of the tickets you buy. It does take more work to do the research yourself, but it is worth it if you want to save money!