Use frequent flier miles to get an upgrade to first class, rather than for more flights. This lets you fly first class for less or possibly for free, depending on the airline and the amount of frequent flier miles.
Be flexible. See where the more inexpensive flights are going. This should mean first class will be less expensive as well. Another option is to shop around different airlines to see who has the cheapest first class tickets to the desired destination. Your chances of cheaper first class tickets are better when you are flying at a less desirable time of day, or during your destination's off season.
Book flights last minute. However, don't attempt this unless it won't be a big deal to walk away from the idea if it doesn't work out. Sometimes airlines will charge less for first class tickets at the last minute, rather than let the seat go empty for the flight. Other times, last minute flight tickets will be very expensive, depending on the season and location, so use caution with this method.
Ask the travel agent or airline when booking a ticket whether there are any promotions or discounts going on. Airlines sometimes do this to compete with one another. Call a few airlines to ask about these promotions.