Michael Horton has written a paper on constructing good arguments (and avoiding bad ones) for his students, and has cut out some of the essay-specific things to produce a short little set of guidelines for engaging well with people:
Especially in a “wiki” age, our communication today is prone to gushes of words with trickles of thought. We don’t compose letters much anymore, but blurt out emails and tweets. Just look at the level of discourse in this political campaign season and you can see how much we talk about, over, and past rather than to each other. Sadly, these habits—whether fueled by sloth or malice—are becoming acceptable in Christian circles, too. The subculture of Christian blogging often mirrors the “shock-jock” atmosphere of the wider web. “Don’t be like the world” means more than not imitating a porn-addicted culture, while we tolerate a level of interaction that apes the worst of TV sound-bites, ads, and political debates.
For my seminary students I’ve written a summary of what I expect in good paper-writing for my classes. It follows the classical order of grammar, logic, and rhetoric. It also explains why the pursuit of excellence in thinking and communicating is not just an academic exercise, but is a crucial part of Christian character.
It’s a bit technical at points, but it’s worth a read to help you identify arguments and engage in discussions online or elsewhere.
(And before anyone asks, no, this is not directed at anyone in particular.)