Trolling from a kayak is different than trolling from any other boat. The big difference is that you are providing the power. Setting the fishing lines is the same. One rod is setup and placed in a rod holder. Then the other rod is setup and placed in a rod holder.
Next you cover water with multiple trolling passes. This is a very effective technique to catch fish.
The kayak pictured above is a Hobie Pro Angler and the drive is called Mirage Drive. The fisherman operates peddles that move fins under the kayak in a scissors like motion to propel the kayak. No paddling and hands free fishing.