There is a limit of 10 pending friend requests at a time.
You can click on a member's username wherever you encounter it—whether in your game archive, live chess chat, or by searching for their username on the Members page. Just click on the 
icon
You can also send an invite from the member's profile by clicking More and selecting Add Friend:
The member you sent the friend request to has three options once they see the request: Accept, Decline, or Ignore.
If you've sent out many invites that haven't been accepted, you won't be able to send more friend requests. Check out this article for instructions on canceling a pending friend request: How do I cancel a friend request I sent?
Mobile
If you have recently played a game with the person you want to add, or are in a game with them now, tap on their avatar and choose Add Friend:
If you have never played with them before, but you know their username or email, you can add them through your friend list.
Tap the
icon on the top right corner of the homepage screenType your friend’s username into the search bar
Tap Add next to their name to send them a friend request - Once you have sent the request your friend will need to approve it
Check out this article to learn how to unfriend a member: How do I remove a friend?