Using the API of relations module
Unfortunately the relation.api.php file included with the module is empty, so it doesn't appear that there's any official API documentation yet. There's the standard documentation but I don't think that covers code.

In this situation I normally head straight for the .test files included with the module. If they've been done properly (and it looks like they have for Relation), you should find all the code examples you need in there.

To find out what hooks (if any) the module provides, I usually just grep the module folder for module_implements( and see what hooks are actually invoked. If any are provided by the module you should be able to find them that way.

If that doesn't help it might be wise to re-think your question and make it more specific to what you're actually trying to accomplish in the first instance.