Great question! Basically, you can get an upgrade one of three ways...
Keep in mind that all three of these possibilities will never GUARANTEE you a larger car at no extra cost. Even free car rental upgrade coupons state that the upgraded car is subject to availability at the rental counter.
I would say that the easiest way to get a larger car for fee, is to reserve an economy or compact car. Companies generally overbook these sizes are are more likely to upgrade.
But, also keep in mind that they may offer you an upgrade at the counter...for a small fee. Just say no, if you are ok with the small size. That way, IF they NEED to upgrade you, based on availability, they can't charge you. This assumes you are ok, if the compact is available and is the car you will receive.
Hope this helps!