ID-ing users on a network

I need to be able to identify each user on a network by machine by time of day, etc.

Is there a way or a program that I can use that will allow me to identify the users of each pc on my network after the user has logged off. I network a high school and there are frequent problems on pcs caused by students who may be malicious and attempting to cause problems. Also, there are those who just do not know that their actions will cause machine problems. I want to be able to identify what student was using what pc after the fact. Thanks for your help.