The new feature was announced September 22; see Stay in control with Block and Unsubscribe. The feature is easy to use. On your computer, go to Settings, then to Filters and Blocklist. Blocking is the second option on the page as you can see from the screen shot to the right.
Gmail will be rolling out the new feature to use on handhelds over the next week.
Addition, 8:13 pm: You will see in the image that the way to block senders is to block them from inside the conversation. Open the email and on the upper right side of the message (where the reply arrow is), click the More down arrow and the Block function is there.