There are a couple of ways to track this kind of data in Clarizen.
In the People module, you can can add (gear icon > manage) columns such as users Last Login date:
You can track fields on your work items such as: Last Update By/On or CreatedBy/On.
I can also suggest having a look at our Audit Trial for Work Items app: http://www.clarizen.com/appsmarketplace/item/Audit-Trail-For-Work-Items.html that records changes of % complete, start date, due date as well as time of change, who performed the change and the previous and the current value of work items in 'Recent Activity' field. Please note, you can tweak that rule and add additional criteria that will fit your requirements.
Last but not least is Timetracking. For instance using a Stopwatch feature allows you and your users to record, in real time, the time being spent on any Timesheet Reportable work item.
Please find more info here: