Search for the lowest published fare for your trip through the online search engines such as Orbit, CheapOair, or Priceline. Try to find at least three different low fares for comparison.
Talk to your Travel Agent for the lowest fares and ask if you will get reimbursed if the ticket prices goes down after your purchase.
Be willing to work around the restrictions set by the airlines such as the date and time you want to travel, lay-overs, one-way or round-trip, etc. Being flexible in this area can yield lower fares.
Ask the Travel Agent to look up Y-Up fares, full coach with free upgrades and the fare codes A,D,I, or Z. These codes are heavily discounted business and first-class fares. Be flexible with your airports if you can fly in a few miles away from your desired arrival point, this can save you money.
Look at your prices and upgrades that were offered to move from coach to first-class and make your reservation and enjoy first class travel on a coach fare.