There is no objectively correct answer to this question. If we knew for sure how to conduct this “war” we would be much better off.
My view is that we need to conduct this war much as we are doing it now, only with a bit more emphasis on political measures. The “War on Terror” can be conducted in two ways. It can be conducted militarily, through intelligence gathering, drone strikes, and the like. On the other hand, it can be conducted politically and diplomatically, through efforts to ensure that the Muslim countries, and average Muslims around the world, see the United States in a positive light.
Both of these are surely necessary. We should continue to be very aggressive in finding out who the terrorists are and where they are. We should aggressively try to prevent them from getting financial support. We should, if we cannot capture them, try to kill them when it is important to do so. At the same time, however, we need to be more aware of how we are viewed in the world. We need to do what we can to try to get potential terrorists to stop seeing us as the enemy.