Commentary can be a hard concept to understand without examples to guide you. Beside the wonderful examples and explanations presented in Richard Straub's and Summer Smith's articles, I have included links to some of my own commentary and the papers on which those comments were based.
Examples from Straub's article
Straub's example of Directive commentary
My first commentary: Complete with evaluation from my professor and trainer Dr. Essid, this commentary is a good example of directive commentary.
My two page commentary: This commentary tackles an "offensive" paper that needed a lot of revision.
My English as a Second Language commentary: This commentary is a combination of directive and facilitative commentary because of the unique ESL field. For more background on ESL take a look at a project complied by my classmate John Lee.