Step One: Take any 8 of the 9 coins, and load
the scale up with four coins on either side. If
the two sides are equal, then the remaining coin
is the fake.

If however, the two sides are not
equal, then that remaining coin is a real coin and the fake is in one side or the other of the scale. The trick
is that now you must unload at the same time a
single coin from each side of the scales. If the
scales now balance, the bad coin is one of the
two which you just withdrew. If the scales
remain unbalanced, the fake is still on the
scales. As you remove good coins you can just add them to the good coin pile which began
with the first isolated coin. Once you have
found the two coins which when removed balance
the scales, or if they are the final two and the
scales are still unbalanced, you take one of
those two and weigh it against a known good coin. If they balance on this second loading of
the scales, or if the don't, you have now with
only two loadings of the scales correctly identified
the fake coin.