The easiest way to block someone is to click on their username, then select 'block' from the menu that appears. (you may have to click 'more' to see this option)
If the member is on your friends list you will first need to unfriend them before you see the option to block:
Once blocked, a member cannot do any of the following:
post notes to your account
send you messages
accept your game seeks
be auto-matched with you in open seeks
join tournaments that you are running
post in content that you created
You can also block users by entering their name on your blocked list. Go to your 'Settings,' then choose 'Blocking' This will lead you to this page:
(https://www.chess.com/settings/blocking) and you will see a text box where you can enter the name of a user to block.
Below the text box you'll see a list of any members you are already blocking:
To unblock them, simply click 'unblock' to the right of their username.