How are strings allowed to vibrate in string theory?

I have recently been reading up on the basics of string theory and my question is this. How exactly are strings "allowed" to vibrate? In particular, do they have to be in all ten dimensions of space as predicted by M-theory at once? Or can they just "reside" in several of those dimensions?

Please excuse the novice question. I have been unable to find detailed explanations of string theory without math that is way over my head. On that note, if anyone has any suggestions for introductory books/textbooks on string theory that are between the simple popular books and the extremely complicated textbooks aimed at graduate students I would really appreciate it.

Thank you for your time.
 

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