EDIT: I read and submitted this too fast yesterday, as pointed out by comments. I stand by what I said here as being correct if the actual ending part were a plural noun phrase, but it doesn't answer the question being asked. Look to the accepted answer above to answer this question.
You're right that "here are how" is correct, for the reason you give. This article goes into more detail.
In written language, you should normally write it this way. However, I don't think most people would say it that way. I would definitely say "here's how" because it's shorter, and I don't think I'm the only one. So, if you're trying to reproduce dialog, you can use "here's"; otherwise, use "here are".