You asked how to FIND the CG of an airplane. That is completely different from checking to see if the plane is balanced properly.
To find the CG of an airplane, the easiest way to do it is to suspend the plane by the wings from a single point in the ceiling. Then, with the datum line level (I usually just level the tail, if it is a flat-top tail, and the incidence is set at zero), hang a plumb-bob from the point of suspension. The plumb bob will point exactly at the center of gravity for the airplane.
Now, if you want to check to see if your plane will fly right, then the CG of the plane must be within the acceptable range as set by the manufacturer (or as calculated as instructed above). If the CG of the plane is behind the recommended point, then the plane is "tail heavy." If it is in front of the recommended point, then the plane is "nose heavy." Remember, CofG is a point on the airframe itself, it is NOT a number that you calculate. You try to MAKE the CofG on the airplane the same (or close) as the number you calculate. CofG is also a 3 dimensional point, not just a 2 dimensional point that most people think of it as. However, when balancing the airframe for proper flying characteristics, using the 2-D model works just fine, and there is no reason to ever try and find the 3-D CofG on a model.