In Live Chess, you can see your friends on the "Friends" tab. (They have to be in live chess at the same time as you for you to see and challenge them there.)
On the Friends tab, you can click "Play" on the Actions menu to challenge them (if it says "Watch" instead of "Play" it means they are already playing a game, which you can observe).
You can also click on the friend's name - both on the tab and in chatrooms - to get a menu that includes "Challenge."
If you don't see the Friend tab in live chess;
If you can use the gear wheel icon (looks like a flower head) next to the chat tab then click on tabs. Then check the box you to show on your tabs in here, like games / players / all games / friends etc. Its your choice which ones to check, which ones you want to see on your tabs.
(remember to save changes on the box below it and they will always show when you log in.
How can I challenge a friend to play live chess?