Rolling or folding and rolling your Oriental rug depends on what your plan is to do with it, for example, are you storing or shipping it? In our Oriental rug shop we roll most of our rugs until they are ready to be shipped. Depending on the weave and thickness of the pile some rugs need to be folded before being shipped so that they are not damaged during the shipping process.
The best way to store Persian rugs long term is to keep them rolled. If a rug is kept folded for a long period of time the creases where the folds are become more difficult to remove. Those creases can also weaken the foundation threads eventually leading to breakage and more problems.
When to STOP folding: if you hear cracking or popping. This means you have a potential dry rot situation and you need to take further action to protect your rug. When folding a rug it should be relatively pliable and you should not meet too much resistance (depending on the size of the carpet of course).
Ideally, when storing a rug for the long term it should be rolled around a support tube like an acid-free archival tube or a cardboard rug tube wrapped in muslin cloth.
In our shop we always roll our rugs with the pile facing the inside of the roll. It is best to keep the roll as straight as possible which can be difficult with hand-knotted rugs as some pieces are not perfectly symmetrical. So just do your best to keep the roll straight.
If you are storing your rolled rug long term it is a good idea to wrap it with muslin cloth. Some museums wrap their textiles in a sheet of clear polyethylene which also protects against bugs and potential water leaks. Stay tuned for a guide on storing your rugs.
If you are shipping a 9x12 Heriz carpet you are probably going to have to fold it before rolling it! We tri-fold our room-size carpets so our customers don't end up with a large crease down the middle of their rug. Start by folding the carpet into thirds length-wise. Then fold one end of the rug which will begin your roll. This also protects the rug during shipping because the weight is more evenly distributed and the foundation threads are not under as much strain in the center. This tri-fold method also makes the rug slightly more compact.