"I suppose this can be done in Traffic sources > All traffic sources. Am i right ?" sounds about right or in other words, yes 
"I really, really would like to know what specific tweet traffic was generated."
each time you make a new tweet where you want to link to an article on your site, you should run through steps 1-7 and then use the link generated.
If I were you though I would read som tutorial on URL's and query strings to get the know how behind what your doing. that way you won't be shooting in the dark and will be able to write those URL's by hand.
When doing SEO, SEM and SMM its a good idea to have a basic understanding in HTML/CSS and how URI/URL's work. And know Analytics/adwords tool set by heart.
To be a good SEO: you should be able to read and write HTML, CSS and Javascript + have a basic understanding of DNS records and domains.
To be a great SEO: You should be all of the above and be able to write some basic PHP/ASP/ASP.NET and have at least a basic understanding about servers.
Hope it helps. If there is something you need me to elaborate please tell me what and I'll try to do so 