Alright, I'm getting a new computer but I still need/want files from my old one. Now how would be the best way to connect and share these files?

I have 2 computers and a wireless router. The old computer gets connected to the router with a cable. The other can access it wireless. Now I want to share files from the computer with the physical connection. I tried this before with my sisters laptop, but the problem was that I couldn't connect through IP, so I couldn't figure it out.

Any help with setting everything up would be appreciated.