Before you test the multi-user aspects of a client/server application, you should verify the functional operation of a single instance of the application. This is the same kind of testing that you would do for a non-distributed application.
Once you have written scripts to test all the operations of the application as it runs on one platform, you can modify the scripts as needed for all other platforms on which the application runs. Testing multiple platforms thus becomes almost trivial. Moreover, many of the tests you script for functional testing can become the basis of your other types of testing. For example, you can easily modify the functional tests (or a subset of them) to use in load testing.