As a beginner, throwing your driver, fairway driver, mid-range, and approach shots are all essentially the same motion. Instead of having your shoulder squared-up to your target, like you do when you putt, you'll want to point your dominant shoulder at your target with your feet a little more than shoulder-width apart to give yourself a nice solid base. Grip your disc the same way you did for putting. If it's more comfortable for you to curl your bottom three fingers so that the pads of your fingers are against the rim of the disc, that's fine, just keep in mind that it will be more difficult to keep the driver steady and level. The outside-rim of your disc should nestle comfortably in the crease that is formed in the palm of your hand when you grip it.
Again, think of your body like a spring that you coil up. Hold the disc level, slightly lower than your shoulders and bring it back as far as you can past your non-dominant shoulder, away from your target. Your torso will be slightly turned away from your target and your weight will be on your mostly on your back (non-dominant) foot with your arm straight away from the cage.
Begin the throwing motion by shifting your weight forward, rotating your body and pulling the disc across your body. Keep the disc level throughout your throw. As your shoulders open up your arm will come toward the target and your weight will shift to the front foot. At the end of you throw, snap your wrist and release the disc when your arm is straight in line with your shoulders. This line formed by your shoulders and throwing arm should be aimed at your target or slightly to the right of the target. Timing the release of your throw is very tricky and will take a lot of practice so don't get discouraged. If done correctly, the disc will "snap" or "pop" nicely out of your hand. Continue your follow-through so that all of your weight is on ball of your front foot and your shoulders are square to the target. Your throwing hand will be open with the palm facing up. Be sure to keep your eye on the disc throughout it's flight so you can find it for your next throw.
Don't worry about distance or power when you're learning. The Navy Seals have a saying, "Slow is smooth, smooth is fast." This applies perfectly to learning to drive in disc golf. Drivers are made to cut through the air and fly far so you don't have muscle them into submission to get decent distance. It's much more important to focus on form, accuracy and consistency. Distance will come naturally if you have good technique and once you've gotten the hang of thing you can slowly start to a add a little power to your throws. You may notice some other players take a few steps into their drive, but as a beginner you shouldn't worry about this; it will just give you more room for error.
One of the most common beginner mistakes are releasing the driver at an angle so that it falls sharply to the left; focus on keeping your disc level as you throw. You can even tilt it slightly away from the direction that tends to fall (if you're right handed, tilt it to the right just a hair) when you throw. The other error that most beginners make is just throwing way too high; this will steal all the power and distance out of your drives. Discs are designed to create lift so try to keep your throw nice and low to the ground. It is much more rare to throw too low than too high so try to error on the side of throwing too close to the ground.
Every disc golfer has his own favorite driver and if they play regularly, they probably have a handful of drivers for different situations. If you're ready to commit a few extra bucks to your knew hobby, it would be a good idea to get a couple of different drivers. That way you can learn what suits your style best and have a spare in case you want to introduce your friends to this amazing sport. In addition to the Leopard that I recommended in part one, I like to recommend the Teebird or even the Wraith for beginners who seem to be getting the hang of it or have plenty of power behind their throw.
Thanks for reading, I hope I've eased your learning curve a bit. Remember that the most important thing is to have fun out there.