The most direct way for you to be able to obtain free airline upgrades is to earn them via customer loyalty programs with the airline you fly most frequently. Airline upgrades are generally one of the incentive perks that are comparatively easiest to earn on most airline carrier reward programs.
One way is to complain to the airline about something; if they've given bad service, lost your bags, etc., and you call or write to them and are sufficiently persistent, sometimes they'll give you coupons for free upgrades or discounts.
The best way to get free upgrades from any airline is to join that airline's frequent flyer program. Although the exact details for each program vary by airline, most of them are free. Over time, you usually accumulate miles which can be used for upgrades. Some plans also let you get miles by using a particular credit card.
There are two easy ways to get a free airline upgrade. First, sign up for every airline's frequent traveler program. Flight upgrades are among the first awards. Second, when a flight appears full, sit or stand near the flight attendant near the counter. They will ask for volunteers to be rebooked. Often, a free upgrade or ticket is offered.
Many times, if the flight you are about to board is not full, you can ask the attendant at the desk if he/she could upgrade your flight and if you have been delayed for any length of time, they sometimes are more willing to do the upgrade. Other times, they will announce free upgrades during the boarding process.
Become a member of your airline's frequent flyer program. If you can reach 'elite status, the you will gretly improve your likelihood of getting upgraded it there is any availability on the day you fly. Airlines will give upgrade priority to their to their top tier members. Avoid flying form your carrier's main hub if it large airport.