Read from here: https://www.ads-software.com/support/topic/33189#post-187724
The first step is: BACKUP your database
The second step is: Download [1.5.1.2] Unzip it.
The third step is: Open the unzipped folder, and DELETE wp-images. (You have no need for these in an upgrade)
The fourth step is: Now open your ftp program and go to your blog directories
The fifth step is: On the server, delete the directories wp-admin and wp-includes. Note: If you have “languages” directory in your wp-includes folder (with .mo files) you may want to save/backup those before deleting the wp-includes directory. Upload the new ones.
The sixth step is: The Classic and Default themes have been changed slightly so if you wish to, you can upload those to your wp-content folder.
The seventh step is: On the server and at blog root, delete the old WordPress files and upload new ones. I recommend you do this one by one if you are not sure. Do not delete wp-config.php.
The eighth step is: Now run “www.example.com/wp-admin/upgrade.php”
Honestly, I don’t see what’s difficult to understand about that. You start deleting files from your server in the 5th step in this order:
1. /wp-admin/
2. /wp-includes/
3. The WordPress files in the blog root. (IOW, those that end with .php and belong to WordPress in the blog root.)
Do not delete wp-config.php and /wp-content/.