How does the direction of the changing magnetic field effect the direction of the induced current?

Answer 1

You use the right-hand rule. If the magnetic field is curling counterclockwise, then the direction of the induced current is "up". If the magnetic field is curling clockwise, then the direction of the induced current is "down".

What doesn't change is the fact that the magnetic field is ALWAYS perpendicular to the induced current.

Answer 2

Following LeChatelier's Principle (or Lenze's Law if you like):

If the magnetic field is Building it induces (an EMF which produces) a current that opposes the build up.

If the field is collapsing - it sets up a current (or EMF) to oppose the collapse and keep the field the same.

To figure out the directions always Remeber that the magnetic field goes like a corkscrew round the wire as it passes in the direction of the current, or like a woodscrew as it advances.
Then draw the magnetic core, draw the coil and a single wire within it and figure how all the turns working together produce the solenoidal field.
All this is much easier than learning Rules, and gives a feeling for the magnetism.

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