As a basic rule, you are not going to succeed. However, there are certain rules that the airlines use and you may be lucky enough to become one of the exceptions. This article gives three ways to improve your luck.
Loyalty programme
Airlines may consider check-in upgrades for their frequent flyer members. So, if you are on their loyalty programme, and particularly if you are not on the first tier, that would be in your favour.
Note: Loyalty to a particular airline has pros and cons, as with anything, so before you decide to fly with one airline frequently, to get a slight chance of business class upgrades, you might want to check on their average prices. It could be costing you too much for a slight chance at an upgrade.
I have heard of at least one case where someone joined the loyalty programme at the airport, prior to departure, then parlayed that into a business class upgrade. They had no intention of actually being part of the loyalty system, or necessarily even using that airline again. But because he was now seen to be a priority customer, he got the upgrade.
Arrive at the last minute
Here is one tip with an obvious disadvantage: arrive late at the last minute for check-in. You could get upgraded if the flight is over-booked. Why? Because the odds are if its over booked, and you’re dashing to make the counter before it closes, that your seat has been given away. Of course, the risk is that business class may also be full. You may have to travel on a later flight. However, if you are ‘bumped’, it is standard practice for passengers to be given a free flight voucher as compensation. Of course, for that to happen, you have to arrive before check-in is actually closed. If you arrive after check-in has closed, you have missed the flight and get no compensation.
Ask!
Lastly, we can always ask! At check-in, you can ask what the possibility is for an upgrade, and depending on the airline rules and how good a day the check in staff are having, you may just score it. Some people do have the most amazing luck in this regard. You may need to practice being charming. (Like everybody else, check-in staff can exercise their authority for good or for evil. If you fight with them, they have interesting ways of making sure that you lose.)
Good luck