You don't say what type of Database you are using and I'm not familiar with all of what the server logs will tell you, but if you want to see what changes are made to records within the database, then a log table inside the db would be the most appropriate way(assuming the server log's don't tell you what happens specifically within database records).
You should be able to grab the userID from the server and then use methods consistent with the type of db(sqlserver or Access or whatever)to record changes made by users.
I personally wouldn't want to try and do this using ASP. Databases generally have very adequate internal methods to do this. Then if you wanted to see the changes from a page, you could use ASP to pull the data back out of the db and display it.
To be more specific, you would have to give us more info.
Paul