You'd be a roughneck. Typically that means, tripping pipe, keeping the rig and all its components clean and maintained, helping monitor the mud and making the proper additions to the mud, etc. A roughneck does a lot of things really, and if you're looking to learn a rig, there is no better way than to work on one.
If you have designs to one day be in operations for an operating company, the experience of being on a rig, even if only for a short period of time, are invaluable. Before I came to the office I had a good deal of rig time, as a roughneck then as a fishing tool supervisor, and that experience has helped me beyond measure in my career. That, and the fact that if your field people know you've spent time on a rig, they can identify with you, and you with them, a little better than if you went straight to the office out of school. There really is no substitute for having field level experience, both for your own knowledge and for at least some amount of respect from the field personnel.