If you get something like
this package, you won't need anything else (or your existing modem).
Connect the router to the PC with an ethernet cable (probably supplied) - configure it as per the instructions which are usually quite straight forward. Once that's done, plug the USB adaptor into your laptop, again follow the simple (hopefully!) instructions and you are away.
Later on, if you wish to site the router away from the PC, you could install a wireless PCI card into your main computer. Not necessary, but sometimes convenient.