If you only want to change your site from
mysite.com/ to blog.mysite.com
than its fairly simple, as you are not changing the wordpress installation directory.
1. Create a subdomain – blog.mysite.com
2. Create “A name” record for the subdomain blog.mysite.com
3. WordPress
for Single Site > Settings >> change the website url
for Multisite > Mysite >> Network admin >> Sites >> edit url to blog.mysite.com
However if your changing Server or installation directory or folder than the instructions will be different.
Hope it helps.
