Most feed readers know how to read that, so you can paste the URL of the blog itself into e.g. NetNewsWire and it will locate that rel="alternate" link and subscribe that way.
Follow links to articles on blogs from places like Hacker News. If you like what the author is saying, subscribe - then watch out for other blogs they reference in their future writing.
Try to find link blogs, since those are more likely to help you discover other things to read.
I view the webpage source and search for the strings "rss", "atom" and "feed" until I find one. I currently have 145 feeds. I follow blogs, news, I get updates about local events, I follow youtube channels, I get notified about new releases from various github repos, follow updates on various status pages, follow various subreddits etc.