I'm creating a website for a friend and want him to be able to update a blog that's on the site. Is there a tool or way for him to update a blog on some other site such as Tumblr or Wordpress and have the posts from there show up on a page of his site?
There are plenty of ways to do it, but why haven't you installed some sort of CMS on the website, when you're actually the one creating it?
WordPress is awesome for blogging, and you should get it installed on the website instead of trying to get it embedded. Why would you want that anyway? It is usually a horrible solution.
If you absolutely must, you can embed the blog, from wherever via a border-less iframe, which hides it pretty good, but it will just feel wrong, as its impossible to make good UX based on a embedded blog.