If a wave is reflected, the angle of incidence (the angle it hits the mirror at) always equals the angle of reflection.
Take care though: the angles are measured from a line called the normal (the red line in the diagram). This line is an imaginary line at 90 degrees or perpendicular to the surface of the mirror
If we reflect light off a curved mirror, we find that a concave mirror focuses the light and a convex mirror makes the light diverge or spread out.
You can still work out the path of the waves by drawing the normal line perpendicular to the surface and using 'angle of incidence = angle of reflection'.
If a wave enters a different medium its speed will change, this will make the light ray bend.
Imagine a car driving into a muddy patch, if only one side of the car hits the muddy patch, only that side will slow down and the car will turn. It's exactly the same with waves.
If a wave enters a medium it will travel slower in (a lower refractive index) it will bend towards the normal and if it enters a medium it will speed up in, it will bend away from the normal.
The refractive index of a material can be calculated using Snell's Law:
Total Internal Reflection
As we change the angle of incidence of light on a boundary, the refractive ray moves closer and closer to the boundary until it passes a critical point and becomes trapped inside the glass. This is how optical fibres work.
You may find the following Phet simulations useful: