How can I Add and Verify my store domain in Google search?

its a process of verifying your own website or app . you need to make sure you own the website or app to let  you have access at Google search data 

The following link you can access it  through your Gmail account
https://www.google.com/webmasters/tools/home

you can add your site by entering the main search page
then you can choose one of the methods shown in the following picture and should choose other 

Then you can take the code as shown in the following picture for example then click verify

Then you can access your domain data and create a record and place it as the next image