Set up a Blog homepage. Then, in Settings > Reading, set that as the default Posts Page.
Then change the permalinks in Settings>Permalinks.
Next, set up a “Blog” category in Posts > Categories. The simplest way to do this is to change the existing “Uncategorized” category to “Blog.” (You can keep the “Uncategorized” if you really want to; but then, why would you want to?)
The final step is to ensure that all of your blog posts are written as posts, rather than pages. This will automatically add the category /blog/ as a subdirectory in the URLs. When in doubt, you can always set the category in the little widget to the right of the editing pane in WordPress. You can even set up category hierarchies, if you really want to get fancy; find that option in Posts > Categories.
Further Considerations
- If you are changing a preexisting blog to a subdirectory on your site, then keep in mind that, for each page that gets moved to a new location (i.e., www.yoursite.com/blog/post) you should implement a 301 redirect from the old location (www.yoursite.com/post) so that any links pointing to that post will still find their mark.
- It’s always a good idea to keep an eye on what content is being indexed by search engines. (To check what’s already been indexed, try a “site:yoursite.com” search in Google. Not always 100% accurate in my experience, but it gives you an idea.) Often, whenever you publish something in WordPress, all sorts of archive and tag pages get created automatically, each with a duplicate of the content from your post. This can confuse the search engines, because if someone is looking for your content, the engines don’t know which version to display. This is where robots meta tags come in handy; you can use a handy plugin like the excellent WordPress SEO to set certain pages to have a “noindex” robots meta tag. (If this doesn’t make sense to you, consult a reputable SEO. Indexing issues can really harm your site’s performance in search engine results, but it gets technical fairly quickly.)