basically, you need to know:

Swept Volume.
This is the volume your piston travels from top to bottom. This is found by doing the calulation: bore area x bore area x 3.14159 x stroke

Clearance volume:
This is teh volume above the piston at TDC. This is best found by filling it with a fluid.

You then do the calculation:
CR = Swept volume + Clearance volume / Clearance volume.

I have pics somewhere to show using a burette i expect if you need to see one.