You can block someone from calling or texting you one of two ways:
To block someone who has been added to your phone's Contacts, go to Settings > Phone > Blocked > Add New. The All Contacts window will appear where you can scroll through names to then tap the name of the contact you'd like to block. You'll be taken back to the Blocked window with the name added to the list of blocked contacts.
From Settings, contacts can also be blocked selecting either Messages or Facetime, and then following the above instructions.
In instances where you want to a block a number that isn't stored as a contact in your phone, go to the Phone app > Recents. Look for the number (or name) you'd like to block and tap the blue "i" with a circle around it to the right of the number. Scroll down to the bottom of the contact card that appears and select "Block This Caller." The message "You will not receive phone calls, messages, or FaceTime from people on the block list" will appear with two options: Block Contact or Cancel. Hit Block Contact to add the number to the big, bad blocked list.
Block from Messages by selecting the message thread with the contact and tapping Contact in the upper right corner. Select the information icon, and proceed with the same instructions as in the Recents tab in Phone.
