So what I would like to do is, move the content of example.com/blog to yolo.com/blog. The yolo.com website is already live and has contents in it. So I just want to move my existing blog to a subdirectory on yolo.com. I have access to the Cpanels of both websites.
You need to create a database (with the corresponding username and permissions) in the cPanel of yolo.com, so your blog won't interfere with whatever you have in yolo.com. MySQL Assistant of cPanel is very easy and fast.
You need to download and install WordPress in yolo.com/blog folder. In your cpanel this usually is public_html/blog. Install WordPress.
Once the database is created and WordPress installed and running properly, you can start the migration. I recommend to use this plugin.
Important: there are many methods to achieve what you intend to do, I think the one described here is the most convenient.
Is yolo.com a WordPress site ? If it's a Wordpress site, you can use Wordpress importer plugin to export content from example.com and import them to yolo.com .
example.com and yolo.com need to be online when you import your content
Dont' forget to add on .htacess file of example.com this instruction to keep your SEO and redirect users to yolo.com :
Redirect 301 /blog https://www.yolo.com/blog