Let me start with the obvious - before we construct a comment, we must read the article, blog entry, other comment or whatever. Obvious, blindingly obvious, but oft times obviously not undertaken. Many a time one sees the spam comment - everything to do with promoting something that has, at best, little to do with what has been written, or of little content or benefit. As a writer you should always rid yourself of these anathemas.
Whilst reading, one must undertake what was taught you at school - comprehension. I write from a background of logical thinking, that I transformed into computer programs. I write formally. My style is not always the easiest to follow, because I tend to write long, complex sentences with analytical constructs. Your comprehension skills will be sorely tested when reading my missives. However, if you wish to comment successfully, you will need to comprehend all sorts of styles, across a myriad of platforms.
Once you have read and understood, you should extract one, just one, item to comment upon. It should be something, if possible, that reflects your knowledge-base, and once enumerated, shows you in good light with the audience you target personally.
The comment you make should be in your voice. The one you utilise elsewhere on the net. It should be more than just succinct. The more you write, the more likely it is that the recipient knows that you have taken time out from your busy day to make an effort to extend the debate, conversation, comment thread. It must be relevant.
If you found more than one thing to comment upon, then leave the further item/s to subsequent comments. Why? So that threads do not show confused messages or thought processes. It is easier to process one thought at a time, than to process multiple streams of thought (unless, of course, you are female).
How to comment is not about just making a comment, it is about making a relevant comment. One that will garner a response. If a response is fostered then it is most likely that your comment will not be consigned to the trash bin. All your hard work: finding a place you feel comfortable making a comment; finding something to comment about; constructing your comment, will then not have gone to waste. Take the time to ensure your comment sticks - and enhances your chances of having another chance to comment in the thread. Questions at the end of your comment are always a good way to push the button of the author, to respond.
You already have the artistry for constructing articles. Use those same skills in constructing your comments. In both cases you are answering a question. Take as much time, effort and thought building a good comment, as you would for your article or blog.