If you look at wire coil down it's central axis (so that coil looks like a single ring) then shove a magnet in this hole, the current induced in the coil will go counterclockwise.
If you hold a wire with your right thumb lying along the wire in the direction of current and wrap your fingers around the wire, your fingers show the direction of the circular magnetic field around the wire.
When the coil is by itself, there's no magnetic field inside the coil, but when you bring the north end of the magnet unto the coil, a magnetic field goes into the coil. All objects tend to resist a change in magnetic flux, so the wire will try to "cancel" out the magnetic field going into the coil, but creating a current in the wire such that the induced current creates it's own magnetic field moves outward from the coil.
If you hold a hoola hoop in front of you with your right hand in such a way that likee a big perfect circle, this can be used to represent the end of the coil. Let your thumb lie along the edge of the hoola hoop and your fingers should now be curled TOWARDS YOURSELF. This represents the magnetic field the coil creates, and the direction of your thumb is the direction of the induced current.