I'm building a new site at the moment, I've never blogged before and I'm not sure what the best practice is with regards to blogging or not. If I have a blog on my site and update it with an article I've written but also give that article its own domain such as mysite.com/article will that affect my ranking with google because their algorithms assume I'm duplicating content? I'm planning on adding a new article once or twice a week, should I just scrap the blog and continuously update my site once a week with an article with its own domain and e-mail users about it?
No,google assume it duplicate content,if your article have many words same with other's content in search engine.simple way to know how your article is unique is after write article copy it and paste in google search then analyze the results that how much words are same with your article words in results.Your article would be good and unique if there is no words same in search results.
You can check your article content for unique in a tool like freearticlespinner and do Directory Submission, Press release and Social bookmarking, etc.
Wait a minute, when you say you are blogging on your website and blogging on mysite.com/article, it is the same thing. That is not a subdomain, it is a part of your main website. So it is not considered as a separate site and your blog will be seen as unique content. Just post the blog on mysite.com/article and you are good to go. Hope that helps.
Scrap using duplicate content as it will only hurt you. I'd make a fresh article once or twice a week as your blogs update.
there is no such thing as "duplicate content!" with the exception of the content within a separate domain. There is a tons of duplicate content on the websites and all of these sites are functioning well. Difference between duplicate content and unique content is that unique content is easier to promote. You can not be penalized for duplicate content by Google, or other SE. Do not trust to what Matt Cutts says, they just try to get you out of the bussines, and make your job hard.