When you login to your admin panel WordPress will show update notification at the top, you can update via clicking on Update Automatically link.
But sometime your server may fails and update stops in between in that your blog may respond in unusual way.
Here is a simple way to update your WordPress blog via FTP, I will use FileZilla you can use any of your choice.
First grab the latest version of WordPress from wordpress.org/latest.zip, now extract files in a folder, now launch your FTP client and connect to your blog’s root directory, we are going to upload the downloaded content here.
You need to upload all download folders and files except Wp-Content folder and Wp-Config-Sample.php file. It will ask your confirmation to over right the existing files and folder with new one, just allow it.
Once your upload is completed refresh your WordPress dashboard and it will ask you to update your Database just go through it and at last you will see that your blog is updated to latest version.
Please take a look at the below video to know more :-