Do crawlers know which copy is original and which is a duplicate? Suppose I write a tutorial and post in two forums. For obvious reasons one has a different date and time than the other. Or suppose that I paint a custom avatar and somebody else copies it.
Google, for example, looks for the content that was published first but also relies on other flags to determine if a website is acting in a way that would imply that they are duplicating your content, often for traffic.
If you posted a tutorial in two forums, both pages would be indexed if the forum sites are on par with the subject of your work. So if you were writing a tutorial about how to photograph birds, posting that content on a photography forum and a bird forum would be related to the content. But if you posted on a Japanese Anime forum where everyone spoke Polish, that page would not be indexed as highly as the other forum sites related to your work.
Google has some great suggestions and tips, however how their algorithm actually works is a trade secret so only they know how it it works but generally it's accepted that there is a score applied to pages and sites indexed, leading Google to understand which one is the original work.
In rare situations, our algorithm may select a URL from an external site that is hosting your content without your permission. If you believe that another site is duplicating your content in violation of copyright law, you may contact the site’s host to request removal. In addition, you can request that Google remove the infringing page from our search results by filing a request under the Digital Millennium Copyright Act.
Bing also relies on traits used on websites to determine if it's a website copying work to draw illegitimate traffic. Source: Bing Webmaster Guidelines