How to check that my Blogger website has indexed on Google search and what's the simple way to rank on Google search?

For Checking That The Blog Is Indexed on Google Search  There Are Many Ways For It. Some Of Them Are..

1. By Google Search Console

Submit Your Site To Google Search Console And Click On Search Button And type Your Url And Then Type Click Test Live Url Add Sitemap Also.

2. By Typing Site: followed By Your Url Of Site In Search

If You Want to manually search for your site that it is indexed or not then you need to google.com and then you need to ype site:https://yoursite.com
replace yoursite.com by your domain this will show you all the page indexed by google of your site 

and for ranking the site top at google you must have rich content organic traffic and goood seo pratices done at your site for read the blogs and learn seo techniques.