The CG location for an airplane is basically an aerodynamic thing. The shapes and sizes "decide" where the weight should be. So you figure out from the measurements of the airplane where the CG range would be and how long it'll be.

About the easiest way to go about this is to go to this online application and plug in the measurements. It's very easy to do. Measure what they want measured, plug in those numbers and it gives you the answer.

http://www.geistware.com/rcmodeling/cg_super_calc.htm

There is nothing magic about CG "machines". They're all basically two sticks. Well, most are. They are one of the most "luxury" of the luxury tools. You can get the most accurate CG location with two long strings, so anything that costs more than that is luxury expense. And you can beat the cost of string by using your fingers.

There are threads all over these forums that go into minute detail about CG locating.