The best way to report someone is by using the steps below.
If you come across any of the following, please report the individual:
Anything lewd, sexually inappropriate, or pornographic—this includes text, images, links, etc.
Anything offensive, threatening, or intentionally discriminatory based on race, gender, sexual orientation, etc.
Anything slanderous, threatening, or malicious toward any user
Anything considered spam like links to unapproved commercial websites, etc.
Cheating, stalling in games, quitting games, or sandbagging
How to Report
From anywhere on the site, hover over the username of the member you want to report and click on the
icon
This will open a new window where you can select the reason for your report - Select the option that best describes the reason you are reporting the person, and write a brief description of what happened in the text box.
If the person is bothering you personally, be sure to check the Block box so that they will no longer be able to chat with you or challenge you to games.
Click the Report button, and the report will be sent to the Chess.com Abuse and Fair Play teams.
When a user receives enough reports of a certain kind, their account will be flagged for review and may be subject to closure or suspension.
If you would like to block someone without reporting them, you can select the 
icon from their profile instead:
Check out this article to learn more about blocking a member: How can I block another user?
Here's a video on how to report or block another member:
Mobile
Tap on the member's avatar in the game to show the list of options:
Tap Report then select from the dropdown in the next menu the option that best describes the reason you are reporting the person - Be sure to write a brief description of what happened in the text box:
When you are ready, tap the report button, and the report will be sent to the Chess.com support team.