If both computers have internet access via the router, then they are already networked and no additional hardware is necessary.
Both computers should be in the same Workgroup. Set any folders that you want to have available over the network as "shared", by right clicking and selecting the Sharing & Security option; at least one folder should be shared in each computer. Any Firewall software needs to be configured to allow access to the networked computers, which may involve adding their IP addresses in a "trusted" section.
If you then go into "My Network Places" set the left pane to show the folder tree and expand the entry for "My Network Places", you should see an icon for both computers and be able to access files in the remote PC.