Induced current in the coil can be increased by increasing the number of turns in the coil, rapidly moving the coil and increasing the applied magnetic field.
Direction of electric current in loops using Lenz's law
When the North-pole of a bar magnet is moved towards a closed loop like a coil connected to a galvanometer, the magnetic flux through the coil increases. Hence according to Lenz's law, current is induced in the coil in such a direction that it opposes the increase in flux.This is possible only if the current in the coil is in a counter-clockwise direction with respect to an observer situated on the side of the magnet.Note that magnetic moment associated with this current has North polarity towards the North-pole of the approaching magnet. Similarly, if the North pole of the magnet is being withdrawn from the coil, the magnetic flux through the coil will decrease. To counter this decrease in magnetic flux,the induced current in the coil flows in clockwise direction and its South pole faces the receding North-pole of the bar magnet. This would result in an attractive force which opposes the motion of the magnet and the corresponding decrease in flux.