 
The gun is mounted to a pan/tilt base. Based on the weight of the gun you have, you can probably get away with a lighter (cheaper) pan/tilt design. This is probably the hardest mechanical part but it should be easy:
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This is a stock Airsoft gun bought for $20 from strikebacknow.com It's all plastic, and uses four AA batteries to power it. You can use any gun you want, I bought this one because it was cheap.
The internals of this gun are pretty basic. The trigger connects the batteries to the motor, the motor "winds" the plunger back. The flat spot on the gear on the right allows the plunger to release, which pushes the air out the barrel along with the pellet.
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Jameco RobotStore has a Servo 5:1 Gearbox for $40 (without the servo) which can move the weight of the gun with no problem. I'm pretty sure you could get by with a smaller mount, depending on your gun size/weight. On the bottom you can see the 90 degree brackets that have been bolted to the mounting holes on the gearbox.
I attached the gearhead to the "magazine" part of the gun. It's a hollow area which is pretty close to the center of gravity. The gun bolts directly to the aluminum hub of the gear using four hard drive screws.
I took a small piece of aluminum to attach the tilt gearhead to the angle brackets of the pan servo. It worked really well.
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The fully assembled gun with pan/tilt assembly. I ended up removing the grip later because it got in the way of the base and the electronics.
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I used some scrap aluminum brackets for the base, and attached the Pololu 8-servo controller to the edge. It's mounted at an angle because I didn't want it out the side, but still needed it out of the way of the moving gun. Note the tape underneath to make sure the circuit doesn't short against the base.
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Since our controller can only control servos (not relays, etc), I took a small servo and glued two switches to it. They're positioned so that when you turn the servo one way, it connects one circuit, turn it the other and it connects the other. This allows for two different firing modes. "fast" and "slow" where slow has an extra resistor.
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This is a Logitech Quickcam Zoom. The camera is glued to the base, which has screws on the corners so that we can align the camera to the barrel later. If I were to re-do this, I would put the screws on the top/sides rather than the corners. Otherwise alignment is a bitch because you can't just adjust up/down, only on the corners.
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The gun with the webcam attached.
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I decided to remove the grip because it was impacting the base and the electronics. So the gun doesn't look as stock, but it makes more mechanical sense. So I moved the safety switch to the stock, the rest of the wiring stayed the same.
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The completed gun! The funnel shown here was a temporary idea to increase the hopper capacity, it has since been replaced with a custom designed bin. The firing capacity is around 300 shots now. The accuracy is on a single shot is about a 1" circle at 10', the accuracy on full auto is about 3".
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