How do laser printers produce the positive and negative charges on the paper?
There is nothing magic about the electron beam, the corona wire, the drum, or the paper. The "magic" is in the coating on the outside of the drum.  It is a special sandwich of materials which are photo-sensitive to the image from the original paper, from microfilm, from a scanned laser beam, or from an array of LEDs.  The combination of charging, exposing, and then transfering to paper is how Xerography works.

All the high-voltage charges have a positive and negative end. The drum is connected to the positive side of the charge, and the toner powder container is connected to the negative side of the charge. So toner is attracted to stick to the drum. When light is focused on the drum it causes that part to lose its charge, so the toner falls off into the waste bin. 

As the copy paper goes near the drum, there is a positively-charged wire under the paper which attracts the remaining (black) toner powder away from the drum and onto the paper.  Then the paper goes through the very hot fuser to melt the plastic toner dust into the surface of the copy paper.