How do instant photographs work?

In order to answer the question of how exactly Polaroid cameras are able to take pictures and have them fully developed only moments later, some information on the structure of the film used in instant cameras is needed.

The Polaroid film itself consists of the same three light-sensitive layers used in conventional cameras, which are separated from each other by dye coupler layers. An image layer, along with a timing layer and an acid layer are placed on top of them. A black base layer forms the undermost layer of all of the other layers mentioned above. Probably the most important layer is the layer situated between the light-sensitive layer and the image layer, which contains a chemical called the re-agent. 
The re-agent is a mixture of opacifiers, which block light; alkali, necessary for neutralizing acids; and white pigments. The entire frame of the film is covered in a combination of these elements. The re-agent itself starts the chemical reaction taking place in Polaroid film.

The chemical processes start once the Polaroid camera pushes the film out, using rollers inside the camera. The re-agent is spread across the whole film, which starts a series of chemical reactions. The colors from the dye layers move up from the lower layers, the acid layer moves towards the top and the re-agent moves towards the lower layers. Another chemical reaction occurs once the re-agent and the acids meet. The alkali and the opacifier in the re-agent react with the acids to make the re-agent turn clear. Following this reaction the image starts to appear until the film is, at last, fully developed.