I want to write a blog post building upon someone else's paper, how can I properly cite/credit them?

As an example, you may be interested in the morning paper, which does exactly that daily for one paper in systems / software engineering / programming languages / AI. Notably, from the entire setup it is very clear that the author of the blog is not the one who originally did the research. The original paper and authors are very clearly named, right at the top of each entry. The blog uses direct quotations fairly freely, but always in a distinct style that makes it obvious which quotes come directly from the paper, and what is the blog author's own commentary.

Even if your setup is a bit different, I think you can learn a lot by incorporating similar principles:

• Put a reference to the original authors and paper very prominently. I would be more explicit that a standard paper-style reference or link - this can get overlooked all too easily by a quick reader on the web.
• Visually distinguish what comes from the original authors from your own text and thoughts.
• Ideally, I would try to pack everything that you adapted from the original paper in subsection(s) of their own, with a big disclaimer at the top.
• Contrary, if you extend the paper, also make sure that it is clear when specific thoughts, arguments, or extensions are your own work. You don't want to be accused of putting words into the original authors mouth.

You have two issues to deal with. If you properly cite and attribute the ideas to the original author, you avoid plagiarism issues. If you don't copy too much, but properly quote, from the paper then you avoid copyright issues.

But, ideas are free to use and to adapt. Simplifying what you find in a paper is a good thing to do.

One doesn't obtain ownership of ideas by writing a paper.

I therefore see no ethical issue at all with what you suggest.

I want to write a blog post which builds upon an author's paper...I want to rewrite the author's examples in simple and more popular programming languages, and use a more casual language...

Such activities are certainly okay and should be encouraged, you just need to properly attribute ideas to the author, which you can do with a standard citation.

You might like to consider co-authoring the blog post with the author, possibly publishing a technical report, which is perhaps more likely to be used by the wider research community.