This is how it would work. A constituent might like to start an electronic petition, so they come up with the idea. There would be an online form to fill out with their information. There could be a drop-down menu of MPs' names and they would choose the MP they wanted, and there you go.
Then it's sent to the MP's account and the staff would look at it. The MP would consider it and say it's good or the MP would go back to the constituent to say the petition needs to be reworked. There's an initial debate and then it goes to the clerk for verification. The clerk might notice for example that there's swearing in the petition and say that it can't be tabled. At that point there is no cost at all to the House.
If the MP says the petition is fine to go forward, and the clerk verifies it, then it's posted.