If the serve motion feels really strange to you, think about it like you are pitching a baseball as high into the air as you possibly can. You can even do a drill where you do an imaginary toss, bend your legs and hips, coil your arm, and then with your right hand, throw a baseball as high as you can. This will help you understand the pronating arm motion of the serve.
Check out this link to a professional baseball pitcher. The mechanics of the serve are virtually identical, except on a different plane.
The hip lead at 9 seconds in is identical to the hip bend on the serve.
His glove hand at 20 seconds is extended just as your left hand would be after the toss.
His pitching arm at 21 seconds is bent and coiled as your racquet arm would be.
At 22 seconds, there is a big stretch in his chest and shoulders as he initiates the pitch through.
The legs and hips lead, followed by the shoulders, and the arm only comes whipping through at the end from 24 to 25 seconds.
At 26 seconds you can see the natural pronation of his arm as he snaps through. This occurs with the serve as well, although it does not help to think about it (See Roddick serve video). The pitcher certainly doesn’t think about pronating his right arm immediately after his relase – it’s just a natural outcome of the movement.
At 31 seconds you can see he came right through, across his body with his right shoulder, and landed on his left foot. This is identical to how you should come through on your serve.