How to use debug log salesforce for a specific class only?

The short answer is, you can't. The class specific debug log salesforce levels only control how verbose the logging for those classes are. When the user executes an action, all the classes within the same context are logged. Theoretically, you can make this easier on yourself by lowering the debug level of all of the classes you don't care about that you expect to show up within the same context but that's still not even close to what you want. You can try to implement a custom logging tool but even then, you're not going to get true logging. You'll only get the information you tell it to give you (which may work for your needs). What I typically do is talk to the user I'm trying to debug. Tell them to stop clicking on things, delete all the debug logs, then tell them to click the one button that executes the action you want logged.