We visited Anne's roof in a previous show where she had three different types of roofs, no flashings and inadequate transitions between each roof, and of course water buckets in the house. In fact one roof was only six years old, the centre part in good shape but the flashings letting in enough water to completely rot away the wood below.
So we watched the placement of a torch applied elastomeric roof by the guys from Avenue Road Roofing in Toronto. Everything was cleaned off. The rotten wood was replaced. Wooden support was provided for the little vertical transitions between the roofs. Then as you see in the first photo, the membrane was heated up (keep that flame away from the very dry wood) and rolled onto the wooden deck. (With that torch up there, you want to really know that you have a trained professional on the roof and that he has a lot of liability insurance. Follow this link to see new requirements for fire protection in an article on asphalt vs. elastomeric roofing.) The drip edge flashing goes over the first layer and under the second one.
On the small roof on Anne first job, the "contractor" stopped there. But this waterproof membrane has no protection against the UV rays of the sun. So they torch on a top-coat membrane that has the granules on the top to protect from the sun. Both of these are sealed with heat to the flashings on the side of the roof.
By the way, if you can't get to the roof space from inside the house, you really should cut a hole in the roof before the job is done, to see just how much insulation you have in this roof. While the old roof is stripped off and before the new one goes on is the ideal time to fix insulation problems. You can just put a temporary patch over your exploratory hole, because you get a new roof in a few days.