There is more than one right way to do it, and everyone will tell you that their way is right. You should probably microwave some popcorn, because this conversation usually gets pretty heated. I will try to cover the main points.
First off, if you're staying at a campground, check the rules and make sure there is nothing specifically prohibiting unloading the camper. Some campgrounds do not want you unloading, for whatever reason. Regardless of the reason, respect the campground owner's wishes. If you don't like a campground owner's policies, vote with your wallet and move on.
Second off, ensure that your camper can be used off the truck. Some older campers were not designed to be used off the truck. Very few, if any, current model campers have this issue.
Finally, if you do unload, it is quite common to lower the camper to the ground for stability and ease of access. Or leave it high. It's up to you. There have been dozens of threads over the years for clever designs of portable plywood stands that do not take up room, as well as commercial products (i.e. "Wobbl-Stopr") so you don't have to lower the camper to the ground if you don't want to.
One final thing, the camper is NOT going to tip over forwards, even with you sleeping in the cabover area.
