Attach a pulse generator and a CRO to one end of the cable in parallel, then attach adjustable resistance to the other end. You will see a reflection from the cable - the edges of the pulse will not look clean, but will instead have a lot of steps. Change the resistance until there is only a single step visible at each edge, this is equal to the cable impedance. Note, to do this you would need a fair length of cable (for an average sort of pulse generator and CRO the rise time might be 10ns and you will need at least 5m to see things clearly).
Cable characteristic impedance depends on a lot of things including the insulation material, conductor diameter and spacing, proximity of other conductors, etc. Complicated subject. Link anyone?
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