Since your left arm is moving horizontally and vertically, and your right hand is moving vertically, body position is very important. The main goal is to be comfortable yet exercise as much control as possible over the motions of the instrument. Some players prefer sitting, while others like to stand (although this can be easily tiring, especially with a big instrument).
When playing the accordion, the shoulder straps should be fairly tight so that the instrument doesn't shift around as you reach for notes. Don't slouch - it looks ugly and causes you to lose control. Your left arm should be between the bellow-strap and the board; tighten that strap (usually via a notch on top of the bellows mechanism, very rarely Velcro might be used) so that it won't cut off your arm circulation, but not so loose that your hand slips as you change directions with the bellows.
Resist the temptation to bend your right wrist and play with your elbow close to the side of your body. Instead, try to hold your entire arm, from the elbow to the wrist, more or less parallel with the keyboard. Though this may seem awkward at first, in the long run it will help you achieve better accuracy because the circulation to your hand is unimpeded. Note that none of this applies to the left arm.
If playing standing up, stand with good posture and adjust the shoulder straps so that the bottom of the accordion is more or less parallel with the floor and the back of the keyboard portion is against your chest. This will help keep it from shifting too much while you play.
If playing seated, adjust the straps so that the instrument rests lightly on your left leg but doesn't hang loosely from your body. The bottom of the keyboard should be between the legs, and not moved too far to one side. You might need to move your right leg out of the way a little bit so the right hand can reach the bottom keys on the accordion unimpeded. Sit up straight in your chair - don't lean backwards against the back of the chair or slump; it looks bad and can result in poorer accuracy.
You might want to consider investing in a backstrap, a small hook-and-eye device that connects the two shoulder straps from behind when you're wearing the instrument. It's useful for bigger instruments because it stops the straps from slipping off your shoulders.