I am assume that your users have to login to the database by using a login id and password, if so;
You could create a table with a user Id column and a date column
When a user logs in write the users login ID and date/time to the table
Putting some form of login in a networked multi user database would be a good idea, not just so that you could identify them, but also adding soem levels of security.
tblUserLog
LogID (autonumber)
UserID (FK to tblUsers)
TransactionType (ie Login/Add/Delete/Modify/Whatever you want or make it a FK to to a table containing the same)
plus whatever fields you need to identify the record the transaction was carried out on, time/date etc.
As smart suggests you then need to add code to all your UI forms that writes to the new table whenever the user does something that you wish to capture (eg when the user opens the db)
NB. If teh database is not locked down properly though (ie they can still get to the tables/queries tabs then the user can do what they like without being logged (including deleting items from your table logging transactions!)