Take the design of your logo to a stamp shop or other vendor that can make a stamp of your logo. Hot foil stamps are commonly used, but a rubber stamp can still work and may be cheaper.
Purchase an ink pad that will go with your stamp, making sure it is in the color you want and will accommodate the dimensions of your stamp. You can likely get the pad at the same stamp shop or many office supply stores.
Place the stamp on the ink pad, making sure the stamp stencil completely and evenly gets the ink on it.
Imprint the ink-stained stamp on the box in the exact location you want it to go, once again making sure the ink is evenly distributed on the surface.
Print out a copy of your logo onto a sheet of paper.
Cut the logo out of the paper, leaving the rest of the sheet intact, to form a stencil of the logo.
Paste the logo stencil onto the back end of a mesh printing screen. The outline needs to be behind the mesh when it faces forward. Make sure the paper covers the rest of the mesh.
Lay the screen onto the side of the box in the location that you want the logo. Pour the printing ink onto the screen.
Press and sweep the ink across the stencil with a printing block, making sure you run the block across the entire cutout area of the stencil. Remove the screen and let the ink dry.