This tutorial explains how to block a contact on Google Hangouts. Once you have blocked a contact on Hangouts, the latter won't be able to see when you are signed-in or get in touch with you. You won't receive notifications or direct messages from this person.
NB: Blocking a contact in your Hangouts list doesn't remove him from your Google + circles; he can still view your posts and photos. Blocked contacts will also appear the group Hangouts you share in common.
Using your web browser
Connect to Google + and start a Hangout session with the contact you want to block. Click on the Options menu (cog icon) displayed at the top right-corner of the chat window:
Click on Block usernamebutton > Block and that's it:
Using the mobile app
This operation can also be performed from the Google Hangouts app. Go to Contacts, select the person you want to block and tap on Hangout message to open a chat window. Tap on the Menu button > People & options > Block username: