I've heard that Google punishes sites with duplicate content.
If I write an article on my blog then import it on Medium (basically a copy/paste) will Google regard it as a duplicate?
Medium.com is a blog platform (sort of).
When Google finds two pages on different sites with the same content, it usually picks just one of them to include in the index. It usually picks the one that it considers the most authoritative. That may not be the one that was published first. If the site where your content is syndicated has good reputation and more inbound links than your site, Google may choose the syndicated copy as the one to index.
When syndicating content you can give Google signals that your copy is the original. This is almost always done by modifying the syndicated copy in some way:
If the site to which you are syndicating does not support any of these, you may be out of luck. It appears that with medium.com, you can at least include a link back to your original article.
Rand Fishkin of moz.com posted an in depth article about medium.com and SEO. The article is long, detailed, well thought out, and well written, so it it probably worth the read. His conclusion is that medium.com can be a platform that can promote your brand, but it isn't great for the SEO of your own site.
I do not know what Medium is, however, for copies of content you will need to use a canonical tag pointing to the original. This is how you tell Google that a particular content is a copy of another.
Google used to take the first copy of any content they found and considered it the original. However, lately, Google has been allowing copies to rank higher than the original. This is why the canonical tag becomes important.
More on canonical tags can be found here: https://support.google.com/webmasters/answer/139066?hl=en
An example can be found under the heading: Indicate the preferred URL with the rel="canonical" link element