Your new PC should have Lan/Ethernet/Network port. Just get a Cat 5e network cable. One end to your PC's Lan port, another end to your one port in your router. Cat 5e cable is very cheap and can be bought in many place including Maplin.
If your new toy has no lan port, you need to follow the following steps (1) Kick yourself becuase you forgot about this (2) Phone the PC seller and ask why an crap PC is sold to you. (3) Get a network adapot (cost under £5) and fit yourself.