Prisms work by refraction.

Light travels at a fixed speed in a vacuum. But within a material, light travels more slowly. You can think of this as something like a wave traveling through a harbor, jostling boats as it goes, and being slowed by the fact that it is transmitted by the way the jostling of one boat reproduces the wave on the other side. The difference in speed is called the refractive index of the material. Air slows light by only about 3 parts in 10,000, but water slows light by about 1/4, glass by about 1/3, and diamond by about 60%.*

When you move a wave, including light, into a region where it travels more slowly, the wave bends. This is refraction, and it's simply what happens when you slow down one side of a wave; there's nothing magical about it. So when light moves from one medium (=material) to another, it bends.

Since the refractive index of some materials depends a bit on the wavelength (=color) of the light, the different colors of light bend by different amounts. That results the different colors (or more properly, different wavelengths of light) in the incoming beam splitting apart and traveling at slightly different angles.

With that model in mind, we can answer your questions:

> If you shine a coloured light what would happen?

In a colored light, not every incoming wavelength would have the same brightness. So you'd still split the beam into its component wavelengths, but some would be brighter than others. Since many possible mixes of wavelengths can produce the same colors, you could actually shine two different (say) yellow lights into a prism and see two different resulting spectrums.

> Why does it need to have an angle if you can use cuboid ones?

Refraction happens even without an angle, but when the light exits the other side of an object at the same angle (as it does if the would-be prism has two parallel sides), the same refraction happens in reverse. This puts the rays back in parallel. Since the rays didn't separate much in their brief travel through the material, all this results in is a very slight violet tinge on one side of the beam and a very slight red tinge on the other, and even that is a result of the fact that the beam has some non-zero width.

If the sides aren't parallel, though, the light doesn't hit the other side at the same angle. This causes the rays to further disperse (more sharply this time, because this time they weren't even striking at the same angle in addition to the wavelength-dependence of the refractive index), which is what produces the widely spaced bands of color you associate with a prism.

> Do different shapes give different affects?

The overall shape isn't important, just the angle at which the light enters and exits.

* You might wonder about the full physics of exactly what's happening here. There are a few ways to think about it.

One is that, in effect, the light is diffracting around all the billions of billions of billions of particles in the material. That diffraction results in an interference pattern, and it turns out that the interference is only constructive at the angle the light apparently "travels" and destructive everywhere else. Since interference patterns are in general wavelength-dependent, it's not too surprising that the refractive index is wavelength-dependent with this idea in mind.

Another is to think of the light as effectively setting up a resonance in the material, with the photons forcing the molecules in the material to vibrate along with the light's frequency. That vibration, which is a vibration in charged particles, produces a vibration in the electromagnetic field - i.e., the original light - but traveling more slowly and with its phase shifted.

When light slows down on an angled surface, it is bent. The more it slows, the more it is bent.

Light of different frequencies moves through glass at different speeds. This means that different colors bend different amounts. If multiple colors are lumped together, then each will bend a different amount, and so they will separate.

Cubes also have angles.

Different shapes and glasses can have different effects. The right shaped "prism" can be a magnifying lens. The photographic effect called "chromatic aberration" comes from the camera lens acting as a prism.

ELI5 + "University project"

Really?

Anyhow, the keywords you need are Refraction https://en.wikipedia.org/wiki/Refraction for why light bends when it enters glass or water etc.,

and Dispersion https://brilliant.org/wiki/dispersion-and-scattering-of-light/

Dispersion is the phenomenon that refractive index isn't actually a constant for a material, but is slightly dependent on the wavelength of the light. This is why prisms split up white light into a "rainbow" spectrum, and why lenses suffer chromatic aberration (unwanted different focus for different colours/and coloured edges on things).