A router can connect multiple computers together on one internet connection. Buy a mid range router, as it will probably give you the least amount of problems. Check reviews first. Dlink, Linksys, any brand name should do fine.
Now either you will have to run network cable. Or use wireless. If its a desktop, you can either use a USB wireless adapter, or a PCI wireless card. Judging by question, I would say you should use a USB wireless adapter, as you dont have to install a card inside the computer. Unless your willing to run network cable ( Using network cable gives you faster transfer rates. And is also a little simpler to set up.)
Follow the instructions included with your router. Setup shouldnt be too hard if you follow instructions.
Edit: lol didnt realize above post wasnt the OP