Beyond this, you'd need to know how to reinstall and reconfigure the programs on the workstation. For example, an email program might need to be configured with the IP address of the mail server, the username and password to use to retrieve mail.
But the basic list above is pretty much all of the core network settings.
In a company (as at home) you should let the computer receive it's initial information from your DHCP server, and/or LDAP. It will default to DHCP anyway so should not need to do anything for this.
If the DHCP uses the hardware address to assign information to a computer, then that will be unchanged if you have not changed the network interface (the network card).
The same can be true of LDAP, I always used the hardware number except on the very limited guest user account. It means a bit more work if a computer is moved to a different appartment, but I think worth the effort.
You should set the client's work group to be the same as the network it is attaching to. ( control panel -> System -> 'Computer name/domain/workgroup )
Apart from the usual network address details (host name and IP) you need to know if it is in a domain. If it is, or you don't know, and you had to ask this, you must not mess with it. you will need an administrator to get it back onto the network.