When you're in the live chess platform, you can create a challenge by using new game options (http://puu.sh/1mhYF) , or you can accept an already existing challenge by clicking on one of the dots on the graph or going to the games tab and then to the seeks menu (http://puu.sh/1mhZd).
Hope that helps :)
"Offering a Challenge - To challenge one player specifically, the easiest way is to click on their name in the 'Challenges' or 'Friends' tab and then using the popup choose 'Challenge to a game'."
In my Live Chess section, I do not have a Challenges tab. How would I challenge a player in Live Chess who is not on the Friends list? Thanks.