I started volunteering in the Peabody museum's invertebrate paleontology collections today. Though there is a hint of projects and research going on, it seems like all the work is to take a fossil out of one box and move it to another box. This is, in fact, what I did for an hour this morning.
I was given a box full of brachiopods. Some of the specimens had their own boxes, but most were grouped in one box with a label, "general brachiopods." Because of how they will be used, they will need to be individually identified and catalogued. Therefore, I learned how to repackage them into individual boxes.
When brachiopods die and get buried in mud, eventually the mud dries and forms a hard shell around... the shell. Then the brachiopod shell, which is made of calcium carbonate, decays, leaving a hole, like a cast. Then the cast gets filled in with minerals, which harden and form the fossil that we find millions of years later. This is true for most fossils (like dinosaur bones): they're actualy rocks that formed in the holes made by the bones. (This is not true for human fossils, which are much younger, and have not yet decayed-- those are actual bones.)
The project I'm helping with is to study this process, called silification, and to find out whether certain species foster the process, and are therefore overrepresented in the fossil record. I'm not sure how involved I'll be in the project part, but it's nice to know that there's a purpose.