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Answer: First, divide the coins into 3 groups of 4. Weigh two of the groups.
If they balance, you know that that the counterfit is in the other group, but you still don't know whether it's heavier or lighter. So, take three coins from the unweighed group and balance them against 3 coins from one of the groups you just weighed. if the second weighing is balanced, then you know that the counterfit is the one that you didn't weigh (from the unweighed group). If the second weighing comes out unbalanced, check to see wether it is heavier or lighter than your group of normal coins (the ones from the first weighing). Now you know whether the coin is heavier or lighter. Take two of the coins from the previously unweighed group (the group that you know the fake is in) and weigh them. If they balance, then it's the one you didn't weigh. If they don't balance, since you know know whether the fake is heavier or lighter, you can tell which of the two it is.
Ok, that was the easy part. Now, if the first weighing comes out unbalanced, you know that the fake is in one of those groups, but you don't know which one. During the first weighing, take note of which side is lighter and which is heavier.
Switch two of the coins, then remove the three unswitched coins from one side and replace them with three of the coins you haven't weighed yet (because you know none of these is counterfit). Now do the second weighing.
If the scale stays tipped the same way, then the fake is one of the three that you haven't moved. if the three you haven't moved are on the lighter side, then you know the fake is lighter. If they're on the heavier side, you know the fake is heavier. Weigh two of the three coins to determine which is the fake.
If the scale tips the other way, then you know it is one of the coins that you switched. Now you only have to take one of the two switched coins and weigh it against one that you know isn't fake and you can determine which of the two that you switched is the fake. (if they balance, then the one you didn't weigh is the fake, if they don't balance, then the one you weighed is the fake)
if the scale balances, then you know the fake is one of the three that you removed. You also know whether the fake is heaver or lighter, depending on which side of the scale you removed those from after the first weighing (remember, I said you had to take note of which way the scale was tipped after the first weighing). Now it's just a simple matter of weighing two out of the three that you removed. if they balance, then it's the one you didn't weigh. If they don't balance, you know whether the fake is lighter or heavier, so you know which it is.