Not a real problem, and it can be done remotely from a central system (can be a desktop), provided you force the users to use their own account.
The log on the DC will tell you when they log on/off the domain. You need to turn on logging on each server, which will tell you the time they logged onto that server, what files they access successfully or not, etc.
You can read these log files from a central location (a server or desktop WinNT4.0 or better system) from each machine in the domain, and can apply filters to find, for example a single user account. There is no practical way to have a central system record all the log ons and accesses to all the systems in the network, the system would totally bog down and would be useless for anything else. Besides, you would not want to do that anyway, it would be too difficult to determne which system it is happening on because of the huge volume of events.
Remember that all logging/auditing consumes system resources, so only do what you really need (for example, if you only care about who accesses a file, only record the successes, not failures, etc.).