There is not a philosophical method, though there are indeed methods, like different therapies. The philosopher's treatment of a question is like the treatment of an illness. To show the fly the way out of the fly-bottle. For solving them means changing one's point of view, the old way of thinking. And if you don't want to do that, then you should consider the problems unsolvable.
Philosophers use a language that is already deformed as though by shoes that are too tight.
One of the most important methods I use is to imagine a historical development for our ideas different from what actually occurred. If we do this we see the problem from a completely new angle. At present we are combating a trend.