I don't do the whole dating website thing... but I did meet my husband through gaming online so I can vouch that it CAN work. I did have a bad relationship through the same means, so I can vouch that it has its faults as well.
Just be careful with the people you meet and make sure you really put stock in any red flags you get from someone you meet.
As far as the etiquette goes... it's very similar to a bar, shopping market situation. You take an interest in someone, is this person throwing hints they are just as interested? Test the waters by starting up a conversation; if the conversation is going well and after a while of getting to know one another throw out the "I really am enjoying our conversations together but I'd like to take it another level, would you like to meet for lunch one day?" -- leave it as something not highly intimate but where you're still able to progress.
If it goes well then you have the opening of, "I really enjoyed today, do you think we can do it again? Maybe even make a dinner date out of it next time?"
In the end, the situation I say above would be very awkward if it was from a woman to a man, but that is my personal opinion. As a southern girl I am more traditional and feel a man should step up and take the lead when it comes to dating.
Hopefully some of what I said makes some sense to you and helps answer your question.