To get started with this, you will first need to register for Google Webmasters
You will also need to ensure your store is not password protected.
Once you have registered, you will need to verify the ownership of your domain with Google. The best way to claim ownership is by using the Meta tag Verification method.
You can initiate this by clicking on Add Property after logging in. You can follow the steps mentioned here
Your site has now been submitted to Google, however, once you’ve added a property and verified it, you can find and submit your sitemap
It will still take some time to show up on Google after it has been submitted, however this ensures that Google has received all your information to display results once it’s been crawled.
Getting indexed is the first step and the next bit is to get your SEO basics in place so as to rank higher in the search results for various keywords. You can check out Shopify’s SEO Basics guide which will surely help.