There are a variety of ways of seeing the world. And there are many worlds to explore. There are dream worlds, there are alternate dimensions, there are possible past or future lives.
There are several different ways of traveling or exploring as a spiritual being. Or, maybe we can say that there are different models. We all dream, so that is the most straightforward place to start. There is nothing exotic one needs to believe in to start exploring one's dreams. One can gradually increase one's awareness of what one is doing during sleep by recording one's dreams, by keeping a journal. Next step is the possibility of Lucid Dreaming. Lucid Dreaming (LD) is when one "wakes up" inside a dream, realizes one is dreaming, but keeps on dreaming, exploring the dream reality one is in. Stephen LaBerge wrote a book about that (Lucid Dreaming), and that is something anybody can do with a little practice.
Then there is Astral Projection (AP) and Out of Body (OOB) experiences. Those terms are often used interchangably. Usually OOB is more concerned with getting out of one's body and exploring the current physical environment. Astral Projection is usually about getting out and exploring any reality, not necessarily the physical world. The most well known authority on OOB is Robert Monroe who has done extensive research and written 3 books about it ("Journeys out of the Body", "Far Journeys", "Ultimate Journey").
"There are two kinds of people in the world: those who are being dreamed and those who are dreamers." (Indian shaman)