The Maxwell equation says $$\operatorname{curl} \vec E = - {\partial \vec B \over \partial t},$$where $\vec B$ is the magnetic field and $\vec E$ is the induced electric field.That may appear, to an elementary student, to be a bunch of gobbledygook, but it means "the electric field curls clockwise around a change in magnetic field;" normally the + orientation is counterclockwise by the right-hand rule; the negative sign makes it clockwise.
Okay, so we need to first define "magnetic field." One popular way to see the lines of a magnetic field directly to look at the effect of the magnets on iron filings, which will naturally show you some "lines" when you bring a magnet nearby; see these images if you've never seen the effect before. The idea of "magnetic field" is basically just that we're going to take these lines and add an idea of "forwards" or "backwards" to them: these lines therefore "come out" of the North pole of a magnet and "go into" the South pole of a magnet. Please reread this paragraph until that convention is firm in your head. You will know it is when you can appreciate that the Earth's North Pole must be the South pole of some big magnet, which is why the North poles of magnets point North: magnets generally want to align with an existing magnetic field, which means the magnetic field at the surface must point Northward, which means it must be going into Earth's North Pole, which makes it a South magnetic pole.
Now you need to understand the change in magnetic field. The magnetic field has both a strength (how close the field lines are together) and a direction (the direction the iron filings point, combined with the orientation forwards/backwards defined above). If a change increases the strength of the magnetic field, like when you get closer to a bar magnet, we point the change in the same direction as the magnetic field. But if the magnetic field gets weaker, then the change points opposite. If the direction of the magnetic field is changing, then we have to also include a component which points perpendicular to the original magnetic field, pointing in the direction that it changes. The full description of how to do this is known as "vector calculus" and I can only give a couple of basic guidelines on how to calculate these "changes" without that framework.
Now: point your left-hand thumb in the direction of the change of magnetic field: then your fingers curl in the orientation of the induced electric field. It is "clockwise" when you look at your hand thumb-on, or when you look at the change pointing towards you. This means that if a current follows that curling, it goes to a higher voltage; or if it opposes that curling, it goes to a lower voltage.
This same "reverse" rule can also be phrased as Lenz's law. This says that induction works like inertia: changing magnetic fields produce electric fields that would cause a current that would oppose the change. As you may know, a wire also produces a magnetic field. The direction of this magnetic field looks like this: point your right thumb in the direction of the current, then your fingers curl in the direction of the induced magnetic field. If you combine your hands together, pointing your left thumb up to indicate an upward change of magnetic field, then putting your right thumb against your left index finger, you'll see that your right fingers curl into your palm, opposite your left thumb.
Lenz's law gives some awesome quick intuitions. For example: the basic electrical component known as an inductor is a loop of wire usually wrapped around some ferromagnetic material. By Lenz's law, when you try to change the current that's going through it, it induces a voltage which tries to keep the same current going through it. It's like an inertial term, it fights any change in the electron velocity. So as you try to ramp up the current, you fight its voltage; as you try to ramp down the current the same thing happens.
