There are three servos.

One to control the turret's left and right movement (X Axis), one for the Y axis (up and down) and one to pull the trigger. Those 3 servos plug into a servo controller which is already included in the software kit.

That servo controller has a RS232 (Serial) port which is old and not found on newer computers so a RS-232 to USB converter needs to be used.

That plugs into the PC or Laptop and shows up as a com port.
The Windows version of the Acer Aspire One ($250) is very small and works great if you don't already have a laptop.

That's the big picture. Now for the details.
Since your application may be different, I left buying the servos up to you. I personally use a Hitec 5645MG for the X and Y axis and cheap HS-322 for the trigger. The small gears I provide in the kit are for Hitec servos. Other brands may have a different spline tooth count and would need to be ordered from Servo City. If you use different servos make sure they have at least as much torque as the ones mentioned and have 180° of travel. You only need 2 screws (included) per servo to mount each servo. Use the pictures below as a guide for assembly.
Plug the servo leads and power in as shown below. I usually scratch an X, Y, and T on the ends of the wire to help identify which is which. It makes no difference which black and white power lead goes where. They both supply the same power from a single battery. see the servo controller instructions page for more info.