To add another ShipWeight client installation to an existing setup you need to run the ShipWeight client installation (can be downloaded from here: https://shipweight.com/download/).
Make sure that you install the same main version as installed on existing client machines. The ShipWeight version can be checked by starting an existing client machine and check menu Help|About…
During installation of the client application, make sure that you point to the existing ShipWeight database server when the installation asks for the SQL Server Instance name. If you do not know the name, check the name on a client machine with ShipWeight already installed: How to Find Instance Name of ShipWeight SQL Database Server.
When you start the ShipWeight client for the first time after installation, the license activation window will appear. Unless you have a standalone license, select the “Network license” option. If the license server for the network license is not automatically filled in, see How to Find the Network License Server Name and Port.