Book as early as possible. Time is the key to get the best Business & First Class deals as the prices are very high when you need to make a last-minute booking.
Fly during the school holidays as business tends to slow down during this period and airlines cannot fill their Business/First Class seats, hence selling them at discounted prices.
Be flexible: adding a couple of days before or after your planned travel dates may lower the fare.
Add a Saturday night stay to reduce the fare further.
Avoid peak business travel days like Monday (morning) and Friday (evening) since these are the most popular times for business people to fly, hereby increasing demand and limiting seat availability.
Book your ticket on a Tuesday afternoon. A study by Farecompare found this was the best time to buy airline tickets as airliners most frequently release discounted tickets on Tuesdays.
Use the airfare search engine Kayak, my personal favourite. The latter checks the price of your requested flight at tons of sites at once, including Orbitz and Cheaptickets, and allows flexibility in your travel dates. However, Kayak does not display all prices, so do not forget to check other airfare search engines and online ticket-sellers as well: Hipmunk, Momondo, Hotwire, Skyscanner, Expedia, and Travelocity.
Matrix is the ITA software that powers Kayak, Orbitz, Cheaptickets and lots of airlines and travel agent’s tools. But you can skip all their ads and come-ons and search Matrix itself for the no-nonsense scoop of flying cheap.
Search for cheap fares on the airline’s official website. This is an often-overlooked tip, but well worth doing as airlines can host private Business/First Class sales that are only accessible through their website.
Make use of the websites Flyfirst, Skylux Travel and Etravelbid which all focus on Business/First Class deals. Etravelbid works particularly well for last-minute travellers, since it negotiates discounted Business Class fares (even up to the day before departure) with no advance-purchase or Saturday night-stay requirements.