For simple stability, you need the center of gravity to be in front of the center of pressure.
You can find the center of gravity by hanging the rocket from a string with a loop that slips along the body. The balance point is the center of gravity. You should measure it twice, once with a fresh engine installed, parachute packed, wadding, etc, (launch config) and again with a burned-out engine casing installed (burnout config).
For simple configurations, stability improves during powered flight, as the engine mass decreasing during burn tends to move the c.g. forward. This explains the phenomenon you might have seen where a poorly designed rocket launches unstably, flies around in circles, then straightens out and flies directly at the most vulnerable object around.
Measuring the center of pressure is more complicated, but Estes has published a Technical Report on how to estimate it here. For a very approximate method, best for axisymmetric models, you can cut out a scale silhouette of the model and balance it to get the c.p., as described in this excerpt from Estes Technical Report 1:
If you really want to get fancy, you could try to rig up a wind tunnel, a mount to hold them out of a car window, etc, etc. The model should be held at the c.g.
You might also find Estes Technical Report 9 "Designing Stable Rockets" of interest.