The easiest way to read and write files on another computer is to enable access to a remote computer's Public folder. To do this, on the remote computer, click the start menu and type "Manage advanced sharing settings". Click on the search result. Open the profile corresponding to your network. Under "Password protected sharing", click on "Turn off password protected sharing," and click "Save changes."
To test this, open an Explorer window and in the address bar, type \\[remote computer name]
If you're curious, you can read Microsoft's page on how sharing works.