What would be a clever way for a character to be transported to another world?

The most realistic way would be to appeal to something like wormholes, quantum branching universes, or simulated reality. These are kind of considered to be sci-fi concepts, but if you do it right you can mix it up and leave the reader guessing whether you're really trying for sci-fi or fantasy. You could even have the character guessing the same thing, even flipping back and forth which each new revelation about their predicament. This can be really fun so long as you don't let it turn into a colossal mindscrew (just hint that it might be one).