I spend a lot of time on the Internet, and much of it is spent arguing with people I disagree with. Here are a few tips if you find yourself in an argument.
Stick to what you know. Don't try to argue quantum mechanics, philosophy, or economics if you've never studied them in depth. It's much better to be honest and unassuming.
Keep it short. No one has the patience to read your thousand word argument. Make your point and quit.
Keep it simple. You may think that presenting three arguments for your position is better than presenting only one. If you do this, the person you arguing with will concentrate on the weakest argunment and ignore the other two. So you are weakening your argument instead of strengthening it.
State the obvious. Don't assume that because a point is obvious to you, it is obvious to everyone.
Check what your opponent has said and if it isn't true, call them on it. Search engines make it easy to double check.
Don't lose your cool. Never reply in anger. Give yourself time to cool down and reply later.
Never forget that your opponent is a person much like yourself. Treat them with kindness and respect.