Soft solipsism dictates that the entirety of personal existence lies inside the realm of sense experience. Everything that you know, think, understand or have sensed or experienced resides inside your mind. This type of solipsism is compatible with, even supported by, a modern physicalist scientific interpretation of reality. The color red, the shape round, the idea of justice or the fact that hydrogen and oxygen make up water -- all of this exists as a mental model inside of your mind. While your body interacts with the outside, objective world, your experience of that world is limited to private, subjective sense experience. This can be an overpowering idea. Everything in the entire world that you are aware of or familiar with either vaguely or intimately, from the people you love to the sciences or fictions you admire to the underlying physical laws and chemical behaviors that govern the known universe, all of this exists, to the fullest extent that you know it, entirely inside of your mind.
And as we have just shown that the senses never and in no manner enable us to know things in themselves, but only their appearances, which are mere representations of the sensibility, we conclude that all bodies, together with the space in which they are, must be considered nothing but mere representations in us, and exist nowhere but in our thoughts. - Immanuel Kant
Hard solipsism takes a further step in that it recognizes and champions the possibility that there is no outside world at all. If our entire sense experience, our entire known, personal universe, exists inside of our mind, then the very evidence that might point to an objective, outside world is itself inside of our mind and of the same substantive quality as all other private existence. Mind is a closed system to a hard solipsist, which cannot be said without reasonable doubt to interact with some other substance or system. The idea that my body is of some non-mind substance, that it recruits the efforts of complex nerves and an even more complex brain to give rise to personal experience, and that that body, by employing the awareness of its mind is then capable of interacting with and manipulating non-mind substance -- these are themselves just ideas, born in and of the mind. It can be easy to see a hard solipsistic orientation as a philosophical or even personal dead-end, a sort of complicated, self-engrossed exercise in futility.
The exit to solipsism is founded in a willingness to accept the consistency of certain sensible systems as being reasonably indicative of the existence of an alternate dimension, its inner nature inherently and entirely unknowable, yet nonetheless impactive on our personal lives and thoughts. It is necessary, too, that we reject certain non-consistent samples of sense experience in preference for these systems — dreams, hallucinations, illusions, uncorroborated memories or other qualia which doesn’t ratify our accepted reality.
That willingness to accept or reject, categorically, certain regions of our personal experience in the absence of incontrovertible evidence necessitating such conclusions could easily be defined as faith.
The exit from solipsism, then, or the ability to exist in the world with certainty of its existence outside of mind is belief in the absence of conclusive evidence.