How do I make a Joomla template K2 compatible or at least K2 friendly?
Is there a manual or guideline for that?

This is a more complex question.
K2 will work with almost any J! template you develop.
Then it pretty much comes down to styling, CSS code. You can use your own CSS file or override the existing.

Should you need to override the extension's view this post will help you
getk2.org/documentation/tutorials/174-templating-with-k2-and-the-concepts-of-sub-templates

www.joomlaworks.net/blog/item/194-k2-inheritance-sub-templating