The easiest way is to run a trace on this user (loginname = 'domain\user'), in the trace you'll have a cpu, read and write column. That'll give you a prety good idea on how much ressources he's using.
If that's too heavy to run (traces might become too big) you can query the dmv sys.dm_exec_requests and sys.dm_exec_sessions to get a snapshot at the current situation (have to query often to get a general picture over time).