Here's how you can use the container snippet code:
1. Open the Webmaster Tools home page and click on Manage site for the site that you want to verify. Select Verify this site. In case you haven't added the site yet, you can click on the Add a site button present in the top right corner of the page.
Please note that you should have "View, Edit, and Manage" account level permissions in the Google Tag Manager to do this check.
2. Select the Google Tag Manager as the verification method on the Verification page and follow the steps on the screen.
3. Click Verify and you are done.
In case you have any questions or doubts regarding the verification method, you can take help from the Webmaster Help Forum.