How do I test the capacitor on a high velocity fan?
A capacitor is defined as two conductors separated by a dielectric. Consequently, there is no direct electrical connection between the plates or conductors. Current only flows to charge the plates by pulling electrons out of the dielectric.

So, on a good non-polarized capacitor, connecting your ohmmeter across the capacitor should show low resistance at first and climb to overload as the capacitor charges up to the voltage of the meter and resistance to current flow increases. Reversing your leads will then yield the same result.

A shorted capacitor will show zero resistance either way.

An open capacitor will show infinite resistance either way.