One method I've seen quite often is to have audit tables. Then you can show just what's changed, what's changed and what it changed from, or whatever you heart desires :) Then you could write up a trigger to do the actual logging. Not too painful if done properly...
No matter how you do it, though, it kind of depends on how your users connect to the database. Are they using a single application user via a security context within the app, are they connecting using their own accounts on the domain, or does the app just have everyone connecting with a generic sql-account?
If you aren't able to get the user info from the database connection, it's a little more of a pain. And then you might look at doing the logging within the app, so if you have a process called "CreateOrder" or whatever, you can log to the Order_Audit table or whatever.
Doing it all within the app opens yourself up a little more to changes made from outside of the app, but if you have multiple apps all using the same data and you just wanted to see what changes were made by yours, maybe that's what you wanted... <shrug>
Good luck to you, though!
--Kevin