The translation of join is rather context-dependent, and I agree that a dictionary might not provide the full details required for every situation.
Regarding the concrete example you cited,
Can I join the conversation?
the translation would be
Darf ich (auch) mitreden?
Darf ich mich einmischen?
There are also some variants like
Stört es dich/Sie, wenn ich mich einmische? (lit. "Do you mind if I barge in?", or more loosely "May I weigh in?" or "May I interrupt?")
sich einmischen literally means to barge in or to interfere, and is used in a somewhat self-deprecating manner here to make the question more polite.
If you have other concrete examples on your mind, feel free to edit your question and we can help out.