When you say “different scene”, do you mean a different .blend file? Or, do you mean a different layer in the same project? I assume the former, since if you knew how to switch layers in the first place, you would probably remember how to get back.
There is an option in the File menu called “Append…” (now “Append or Link” in 2.43). I believe the keyboard shortcut is Shift+F1. From here you can select the .blend file that contains your other object. (That is, if you first open the Character file, then append from the Stage file, or vice versa.)
Once you select the .blend file, you have a choice of what to import, including Meshes, Materials, Objects, etc. If you import a whole object, that will include the mesh and all materials. Before doing all this, it is a good idea to change the default names of meshes/objects/materials to something unique and meaningful to you. E.g., change ‘Sphere’ to ‘Soccer Ball’ or ‘Material.001’ to “Wood”.
I hope this helps. I am no expert yet myself, so if some else has a more lucid explanation, by all means share it.