What type of box? What is it made out of? How is it used?
Please post a picture so that we can see what you are starting with.
Hi ! What kind of box ? A decorative , toy , or trunk ? Do you know what it is made of ? And what do you want to use it for ?
A picture would really help !
Removing the lid would be best but if you can't do that, paint it with it closed. Once it is completely dry, open and paint the interior.
Kathy is right about the how to.
If it's finish is rough you may want to sand it a little. If it's wood any paint will work. If you want a little shine use semi-gloss, for a lot of shine use gloss paint. If you really want shine add a coat of lacquer when box is totally dry.(Think top coat for your nails).
If it's metal use something like Rustoleum. You can also lacquer that.