Neutral (white) wire connection

Use caution when dealing with AC, it can be deadly.

The black wire by accepted standards is the 'hot' wire and will measure (when active) 110-125 volts (in the US) to ground or the white neutral wire in a normal household system.
The white wire may have a couple of volts when measured to an earth ground or any green (or green-yellow) wire which is (by standards) connected to earth ground, often via plumbing pipes in some homes, or a visible or buried grounding rod driven several feet into the earth.

The black (hot) wire is the one customarily 'switched.'

I would highly recommend you have a qualified electrician reconnect the strayed wires to protect yourself and the fan.