I had to read this book as part of our English curriculum back in 2001-2002 (year 7/8).
The story revolves around a female protagonist in her young teens, who meets this guy a few years older than her who appears to have Psychic powers. I seem to remember a scene where Government-types were after him, so he made some game machines in an Arcade display a 3D tiger or something to distract them.
At some point he teaches her how to communicate telepathically, and also how to leave her physical body and go exploring the universe. I remember her describing the ability to turn by moving her eyes, and feeling like a magnet was pulling her back into her body (which got less powerful the further she was away from Earth). They used the 'magnet sense' as a guide to return to Earth and their bodies.
At the climax of the story, the two meet some aliens in space who had discovered the same abilities. They offer to take them both back to their world, however the protagonist's 'magnet' was already very weak, and she didn't like the prospect of never returning to Earth.
Her friend goes with the Aliens, and she returns to Earth. I don't think she ever hears from him again in the end, but continues to explore the universe in search of him.