I'd imagine these are covered by the documentation you're reading, but a few things:

Make sure your classifier function is as lightweight as possible - every connection to SQL server has to run it before it can connect.

If using program_name in the classifier, be aware it can be easily spoofed, and of variations within the name for the same program.

For testing:

You can use GroupId in sys.dm_exec_requests & sys.dm_exec_sessions to find which workload group & resource pool the query is running in.

Perfmon counters in these groups can help you monitor resource governor effects:

MSSQL$InstanceName:Workload Group Stats & MSSQL$InstanceName: Resource Pool Stats

RG is not instance-aware, and only works on the database engine itself.

Note that RG is only really a guide, limits can be exceeded if the server is not under load.