how can an ohmmeter be used to determined if two points on a protoboard are connected?
By measuring the resistance between the points?
Just to extend on Integral's answer, an ohmmeter measures the resistance between the two points using an internal voltage source and a galvanometer, which measures current. If you measure the resistance between two points that are not connected, the current will be zero and the resistance will be "infinite". If the points are connected, however, there will be current and a finite resistance.
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