Go to the ticket counter prior to your flight; the earlier the better.
Ask the counter agent if there are any available seats in the business or first class sections. This might require a small fee. It is well worth it though to book a coach ticket and then upgrade for $100 or so rather then buying a first or business class ticket that costs three to four times as much as an economy class ticket.
Check the pre-flight video display outside your gate. If you belong to a frequent flier program there is a chance you will get a free upgrade. This will depend on whether there are other frequent flier members on your flight who have more miles than you, and if there are any open seats left in first or business class.
