1. Clear your history
Before you search the web for a ticket, be sure to clear your history and cookies. This is important because the last time that you searched for a ticket, the airlines actually know that you are looking to book and they jack the prices up when you return. By clearing your history, you start with a clean slate.
2. Set up price alerts and check prices regularly
Price alerts notify you when the prices of your specific ticket drop or rise. There are a lot of things that could happen day to day that could affect the prices of plane tickets. For example, politics, natural disasters, or as awful as it is, terrorist attacks.
3. Pay attention to trends
Research when the best time to go to your specific destination is. For example, flying to Paris in the months of June, July, or August can cost up to three or four times more than it does in the months of December or January. If you are planning on traveling during that destination's busy season, book your ticket far in advance.
4. Google is your friend
I start looking for tickets by simply googling, "plane tickets from ___ to ____." Google pulls up a list of options from different airlines and I have found that this method typically shows the cheapest tickets. If you want to use a travel fare aggregator, Kayak is one of the better resources. In my opinion, Expedia is one of the worst.
5. Buy two one-way tickets
If none of these tips are working for you, consider buying two one-way tickets. While researching this, also check into flying out of a different airport than you departed from or flying two different airlines.
6. The day you choose to buy a ticket doesn't matter
Rumor has it, Tuesday nights are the best times to purchase airplane tickets. I, personally, have never noticed a difference in the day or time you buy a ticket. That doesn't matter as much verses when you are actually flying. Typically, it's cheaper to fly during the week then it is the weekend.
7. Fly light
Airlines like Frontier and Spirit are great if you don't need a checked or carry-on bag. If it's just a weekend trip, try to fit everything into a backpack and use that as your personal item.
8. Avoid "catches"
The catch with Frontier and Spirit is having to pay for every single thing--from bags to your seat. One way to avoid some of these is to be assigned a random seat for free. Next time, just don't pick a seat.
9. Utilize nearby airports
If you can, fly from or into a nearby airport. For example, sometimes it is cheaper to fly out of Colorado Springs instead of Denver, Colorado.
10. Pay for bags at the same time you purchase your ticket
If you know that you are going to have to check a bag or have a carry-on, pay for it at the time you purchase your ticket. If you wait to do it until later or even at the airport, it will be more expensive.