Write a script that creates a new record in the log table. Set fields in this table to auto-enter the creator account name and creation timestamp.
Set the OnFirstWindowOpen trigger in File Options to perform this script.
Writ another script set to run OnLastWindowClose that performs a find to find all records in this same table that have the user's account name in the creator account name field. Have it enter the current timestamp into a second timestamp field to show date and time that the user logged out.
Note that if a user's copy of FileMaker Crashes, the log will continue to show them logged in.