Let me begin by stating that these are tips I have gathered by posting in many public forums on the Internet and I have learned most of these rules by making the mistakes myself. I'm not trying to point fingers at anyone or act all holier-than-thou. It's a cold, emotionless medium text is. It can be difficult to accurately convey one's feelings when typing a quick reply somewhere. John Gabriel's theory certainly plays a part as well, but I'll try and assume that you are generally a nice person. I also assume that we are talking about a text medium (IRC, forums, Slashdot/Reddit/Digg). None of that fancy voice or video conferencing stuff!
Also, this is not a guide on how to really be an arrogant prick, but just not look like one when you engage in conversations on the Internet. It's also not a guide on not being a jerk. Should you lack basic manners you will have to learn them elsewhere.
Rule #1: Forget the medium
One thing that is quite difficult to do is look past the medium and remember that these are all real people conversing with each other. Don't type anything that you wouldn't say to their face in real life. This is, of course, not exclusive to the Internet.
Rule #2: Remember the medium!
While obeying Rule #1 it's important to remember that in a text medium there is no emotion or tone to our words. If you think that smilies / emoticons are lame and for 12 year olds, well you're right. However, there's no reason for an adult to refrain from using them as well. They can be important quick clues to how your message should be interpreted. You can always rephrase what you write so that there's little ambiguity to your words, but if you're typing something quickly on Digg, Reddit or some forum then you probably aren't spell checking and proof reading each and every post.
Rule #3: Avoid know-it-all responses
Starting a reply with "But ...", "Well ...", "No ...", or "Your mother's a ..." often sounds confrontational. There's obviously no harm in using these in the right context, but many times I have found that removing these from the front of a sentence can drastically alter the tone and make it clear that I am trying to converse rather than argue.
Rule #4: Address the correct party
If you're not speaking directly to the reader avoid using "you" when you mean "one". This is a particularly hard one to get in the habit of doing, for me at least. I am just not used to speaking so formally but in writing it really does make a world of difference. People are defensive creatures by nature and we don't like being singled out or accused. Hell, half of the time we don't even like honest, kind advice.
Rule #5: Accept the fact that people know more than you
Geeks often come across as know-it-alls. While most geeks probably do think they're rather clever (guilty as charged) they probably also know that they don't know everything. When one knows nothing of a topic it's easy to admit that others are right and they are wrong (often because they won't have an opinion on the subject yet). The trouble starts once they learn something about the matter, once they have formed opinions and ideas about it.
I'm not saying that we should all stop discussing things we're not experts on, just that we should try harder to keep open minds about things and realize that others may have some insight we do not. If in doubt, partake in civil discourse and try not to dismiss others without even asking them to back up their claims or ideas.
Cue the comments pointing out how many of these rules I broke in this very post... :)