How to use the rel_canonical tag when two domains point to the same site?

For SEO issues, you must choose one to be your primary domain, and the other you can create a 301 redirect.

Leave two domains separate and pointing to the same site, showing the same content is bad, because Google and other search engines will understand that content is a copy and this causes pagerank to fall.

For your specific case, the canonical tag will not resolve because it can only point to the main content that must be in the same domain where it was inserted.

The most common uses of the canonical tag are:

Page where the tag was assigned: link

<link rel="canonical" href="http://exemplo.com.br/tag-canonical/">

Prevents search engines from understanding duplicate content on the following pages:

• link
• link

I think you could sort out the use of this tag more or less

Just to fry, again, if you have two domains, choose one to be the primary and the other point a 301 redirect to your primary domain.