How to change the sub-title of my blog on Google search results?

I think you are asking about the search description of your blog.
You can create a custom search description for your blog by following below steps.
1. Login to your Blogger account and click on your blog title to open its dashboard.
2. Then goto settings->search preference.
3. Now you will see 'Description' tab. Edit it and write something about your blog e.g., A blog about Runescape MMORPG game, etc.
4. Then click on save changes.
5. Now submit your blog homepage URL to Google index - https://www.google.com/webmasters/tools/submit-url .
Thats all.

Hello.
There are two ways to custmize search description.
First Method
1. Login to your blogger dashboard.
2. Now open setting tab and then search preference.
3. Now open description tab.
4. Write your description here and save.
5. It is only for homepage.

Second Method
when you write a new post or edit a post then in right side of page a search descrition is present.

Simply open it and write your search description and click on done.

Thanks.