To verify your store, you should get an HTML tag from Google Merchant Center (GMC), and place it into your Shopify store. Here's how:
1. Click the gear icon on top of GMC, then click "Business Information" > "Website" > "Add an HTML tag Method".
2. Enter your website URL, pick "I have access to my server", and move on with "Add an HTML tag to my homepage".
3. Copy the HTML snippet and paste it into your theme by going to your Shopify account and clicking "Admin" > "Online Store" > "Themes" > "Active Theme" > "Edit" > in the "theme.liquid file".
Now your store is verified on GMC!