That (Verification Details page) page will show you information about the site as well as a list of any other verified owners. At the bottom of the list of owners, you'll now see a button labeled "Add a user". Click that, enter the user's email address, and that person will instantly become a verified owner for the site! You can remove that ownership at any time by clicking the "Unverify" link next to the person's email address on the Details page.

The new process requires at least one owner who has verified through the meta tag or HTML file. If all of the directly verified owners become unverified, the delegated owners become unverified too.

One more point to note is that the delegated members will have exactly the same access as you have. So, delegation has to be made carefully.