1.  Ask yourself what you are trying to accomplish with your response.  Are you trying to persuade your opponents?  Are you trying to refute their points to an audience that is neutral or somewhere in between you?  Are you trying to clarify your position so that its merits are understood?  Are you trying to bolster the confidence of your allies?  All these are worthwhile goals.  They are also not mutually exclusive.  But being clear on what you are trying to achieve will help you evaluate quite rapidly whether your response serves your goal.  If you are trying to vent aggression and frustration, or prove your superiority, do not expect a sympathetic response from the audience you are using for that purpose.  I would discourage you from pursuing such goals here, but it's not my site.

2.  Consider what the writer you are responding to is trying to achieve and determine whether you want to participate.  If what they write offends you in form, tone, or content, ask yourself whether your response will merely elicit more of what irritates you.  If someone is merely repeating "talking points" for the umpteenth time, pointing that out is unlikely to dissuade them from continuing to do so.

3.  Impute the best possible intentions consistent with the text to the writer you are responding to.  Do so explicitly, as a way to maintain that in your own mind and to obtain a fair and generous hearing from your interlocutor and the others reading your exchange.

4.  Address what is written, not the person that wrote it.  This is especially important to keep in mind on a blog where our access to each other is so very limited.  "I find this point unconvincing because..." works much better than "only an idiot would argue this..."  This also minimizes the possibility of personal insult, whether intended or not.

5.  Do not hesitate to concede a particular point.  Doing so generally appears as strength, not weakness, and will often make your overall argument more persuasive, not less.  It can also mitigate unproductive tension.  Look for opportunities to do so.  You'll get a better hearing from both your opponent and your shared audience.  Communication of respect generally earns it in return.

6.  Take a sentence or two to establish common ground, a point of agreement, as the context for your disagreement.  "We are both clearly interested in expanding access to health care for all Americans.  The difference in our approaches lies in..."  

7.  Don't use any of the above insincerely.  Formulaic civility generally fails.  It appears coercive and manipulative.