You can send a friend request a couple different ways. If you're playing at a table and want to add someone, click on their username. This will open their player information in the chat box. Click on their username in the Notes section to open their profile page.
From their profile page, you'll see an "Add as a Friend" button on the right side of the page under their stats. You can also just go straight to a player's profile page to add them as a friend. Clicking the "Add as a Friend" button will send them a friend request to either accept or deny.
When you receive a friend request, you will get a notification in the top menu bar. Clicking the icon reveals a list with your requests and you can accept or reject the friendship.
You can also manage your requests from this page.