Aerial fireworks are all composed of the same basic structure. There is an external shell container, black powder (charcoal and sulfur), a blasting charge (like a firecracker), the all important fuse, and last, but certainly not least, pellets that have a similar composition as sparklers. The fuel and the oxidizer must be balanced so that the sparkler burns slowly and does not explode like a firecracker. Using different metals in these pellets forms the different colors that you often see, and people can add multiple shells within the whole container that are composed of different pellets to achieve multiple colors sequentially. How the pellets are arranged within the shell leads to the pattern that you see in the sky. The blast spreads the sparkling pellets outward in the same pattern in which they are internally arranged. I have included a couple links that go into more detail, including the specific colors associated with different metals and history of fireworks (wikipedia) and the sparkler composition, lots of pictures, and a short video explaining the chemistry (howstuffworks).

The colors are due to different metals in the fuel for the flame. Each metal emits light at different colors in a flame; most flames are yellow because that is the color that sodium has (and there is sodium in almost everything).

As for shapes, that's due to the shape of the explosive charge and the distribution of explosive. Put more explosive on one side than the other, for example, and the flares on the side with the more explosive will go farther. Making a smiley face just means embedding the eye and mouth flares inside of the explosive; in this way they don't go as far, but putting them on the right side of the center so that they go the right direction.