I agree with most of the posts above, except for the first response which suggests that you pinch the flight plate rather than the rim.
For my forehand, I'm not really "pinching" anywhere, but the majority of the power comes from pressure inside the rim. I only use one finger inside the rim, and the tip of my index finger pushing solidly into the inside of the rim to accelerate the disc. With that application of force you don't need any counter/"pinching" force; the inertia of the disc itself is what holds the disc on your finger. (That way, all of the force you apply inside the rim goes into the disc's momentum, rather than being counteracted by a pinching force.)
The wobble issue has to do with how smoothly you apply that force, and whether the direction of force goes through the center of mass of the disc. For distance drivers, most of the mass is in the rim of the disc, so the height of the center of mass is very close to halfway up the inside of the rim. That means that if your fingertip is centered on the inside of the rim and you push in a straight horizontal motion, the line of force goes through the center of gravity of the disc.
At that point, you just have to focus on a smooth/continuous force and staying in the same plane of motion throughout the throwing motion. (Mike C pointed this out above.) For a flat and level release, I like to imagine that I'm dragging the disc across a level tabletop.
The smoothness of the throw can be messed up by so many factors -- trying to jerk too hard to get extra snap, or even janky footwork. I would recommend practicing the throwing motion with a single step (or just a simple weight transfer with your feet planted) to get a smooth release down.