There are many ways to do this. My favorite way is:
Add a mod_user field to your source table (the one you want to log).
Create a log table that contains the fields you want to log, plus a log_datetime and seq_num field. seq_num is the primary key.
Build a trigger on the source table that inserts the current record into the log table whenever any monitored field is changed.
Now you've got a record of every change and who made it.