To block a friend from exchanging messages with you, tap the friend in the chatting list. Tap the Menu icon (at the upper-right corner of the screen) > People & options. Tap the block icon next to the friend's name, then tap Block.
To remove a friend from the blocked list, from the chatting list, tap the Menu icon (at the upper-right corner of the screen). Tap Archived Hangouts, then tap the blocked friend. Tap Unblock at the top of the screen.
You can also unblock a friend from Blocked people in the Hangouts settings menu.