First, you'll need to remember that a clockwise current generates a field into the page inside the loop. A counter-clockwise current generates a field out of the page inside the loop.
To help explain the description below take the example of a loop in the plane of the page with a uniform magnetic field directed into the page. Over some time interval the field is doubled. What direction is the induced current in the loop while the field is changing?
An easy way to answer such a question is to draw three pictures:
Once you've drawn the To Oppose picture, determine the direction of the current around the loop needed to produce field in that direction. That's the direction of the induced current.
Expressed as an equation, Before = After + To Oppose.
This corresponds to the opposing nature of Lenz's Law. The loop will do whatever it can to maintain the status quo (i.e., it will work to prevent the change).
This pictorial approach works well for determining the direction of the induced current. One problem with it, however, is that it can lead you to believe that the loop is successful at completely cancelling any change imposed on it. This is not the case. The loop fights the change, but it loses the fight in the end and the flux is eventually changed to that shown in the After picture.