If some has sent you a friend request, you will see the notification on the top of the left menu on your home screen, next to the Chess.com logo:
Hover over the Chess.com logo to see who wants to be friends!:
Click on the check mark to accept, or on the 'X' to dismiss. The member will not be notified that you have declined the request.
If you click 'Friend Requests' in the above menu, you will be able to see more information on who sent the request:
On the mobile apps, friend request will appear as notifications under the bell icon at the top of the home screen.