You bomb a drive, but when you get to the ball, you find it smack in the middle of an old divot. First thing: Get over it. It's probably not as bad as you think. Especially if the hole has been filled with sand, you can play a normal shot—with a few adjustments.
The secret to making good contact here is hitting down on the ball. Play it back an inch or two in your stance, and put more weight on your front foot. That promotes a steeper backswing, which, in turn, steepens the downswing. You'll catch the ball first and drive it out (above).
Also, open the clubface a little. This might go against what you've heard, that closing the face helps you dig out of bad lies. But as long as the ball isn't down deep, an open face is better. It'll help the ball jump up and out.
As for the swing, don't be timid. Focus on hitting through the ball. You've set up the right kind of swing with your adjustments at address, so don't try to do anything special. Just think down and through. No reason you can't knock it on the green.
What if you have an uphill lie to the green? That's a good one, as long as you play for it. Take more club, and set the ball forward in your stance. Angle your shoulders parallel with the ground, and aim a bit right (you'll tend to hit this shot left). One more thing: Lean to your front side to offset gravity pulling you downhill. Then swing up the slope.