Some are formed when dead animals are trapped in a layer of mud. Over time the composition of the animal changes and chemicals that normally break down are replaced with other chemicals that don't. The mud becomes stone. A copy of the animal is left in the stone.
It is possible to make something like a fossil in a couple of hours. You can make these with your students and help them identify the once living thing that left the fossil.
Collect together some leaves and shells. Mix one part plaster of Paris to one part of water to create a thick mixture. Pour this into a disposable container. Put oil on to the leaf and float it on top of the mixture. Leave it to set. Remove the leaf and you have a copy of the leaf in the plaster of Paris. To make a plaster of Paris "fossil" of a shell you need to push the shell into some clay in a container. Remove the shell and pour the plaster of Paris on to the clay. Leave to set, and then remove the clay.
Note that your students will need to wear gloves when using plaster of Paris, and that you should not dispose of the unused plaster down a sink.
Another way to make "fossil finds" is to create a mud mixture. Take some soil that has a high clay content and mix it with water. Make a mud pie and embed a shell, a leaf or other textured object inside it. Place the mud pie on the windowsill and allow it to dry out over a few days. When it is dry carefully break open the mud pie to unearth your "fossil".