I am studing this topic and I would like somebody to point me in the right direction for studying this.
Debug Web Parts
This objective may include but is not limited to: ULS log, and event log, debug.log tracing, developer dashboard
This sounds like you're studying for TS: SharePoint 2010 Application Development 70-573.
The part that says what's included are actually practices any development in SharePoint, not specific to Web Parts.
It seems strange to me though, that their list doesn't include the most powerful debugging utility available to a developer - Attaching to w3wp and stepping through your code. It seems they're more interested in having candidates know where log files are kept, rather than actual debugging methods.
Anyway, Andrew Connell did a good blog post on this a while ago for 2007: http://www.andrewconnell.com/blog/archive/2008/06/11/SharePoint-Debugging-and-Logging-Tips-and-Tricks.aspx
For Developer Dashboard, there's plenty about on the web, but first you need to enable it:
Then analyse the output from the Dashboard, here's some info about that:
I think you can just attach the w3wp.exe process to your visual studio debugger and all done.
You should be able to hit the debug point in your code.
You can check the various tools and techniques here to debug any SharePoint 2010 solution :