Pasting Tibetan text

Doing Tibetan in InDesign is non-trivial. But the first thing to try is to turn on the World-Ready Composer. There's a few ways to do it, but I like going to the Type menu and selecting "Apply World-Ready Composers." If you don't have that choice, then selecting your broken Tibetan text with the Text tool and going to the flyout menu in the Paragraph panel and choosing the World-Ready Composer there would also work. 

If these don't fix your issue, can you post again with the name of the font you're using, and perhaps a screenshot of how it looks in Word and in ID? I'd also point out that copying and pasting complex-script text from Word to ID often has real problems (any text at all, really). I'd suggest either using File -> Place to put your entire Word document into InDesign, or maybe investigating the Clipboard Handling section of the Preferences, and trying All Information under "When Pasting..." instead of Text Only.