It is a pretty simple connection.  The end of the cable threads into a part that has a stud on it.  The stud protrudes through the side of the kickdown lever and there is a spring clip similar to the one where the throttle linkage hooks to the carburetor.  The spring clip holds the stud into the lever arm.

To adjust it:
1. Set parking brake.
2. Adjust engine idle speed to factory specifications at operating temperature in
Drive. Make sure someone is behind the wheel with foot on the brake.
3. Throttle must be at idle/stop without choke involvement (warm idle).
4. With the engine turned off, check accelerator pedal height from the floor, which
should be 4-1/2-inches.
5. Again with engine off, disconnect the kick-down cable at the accelerator
linkage, which is the adjustable end.
6. Have someone depress the accelerator to the floor.
7. Adjust cable end so it lines up with the throttle linkage.
8. Test drive and check upshifts and downshifts at normal throttle.
9. If upshifts occur late or not at all at wide-open throttle, the kick-down cable is
too tight. If upshifts occur too early at wide-open throttle, the kickdown cable is
too loose.

Briangillen wrote:

Thanks Steve. Looking at the drawing and comparing it to whats on the car and it appears that my accelerator shaft has been damaged. Thats why the linkage won't connect. I'll try this after I replace the pedal assembly. Brian.

also make sure the throttle is opening all the way first. if it is not, adjust this first.
 

Tell me more. Why is it so difficult?

After further inspection I found the kickdown was missing this part. Fixed for less than a dollar how often does that happen!