Once you click the Search button, you will be given a list of players who matches the username that you searched for. Choose a player and click “Challenge”. Once clicked, a pop up message will show which says, “Challenge request has been sent to (name of player).” Click OK and wait for the player to accept your challenge request.
For Chess, you can access the PVP feature by first choosing Chess from the main lobby. You can access this by clicking the fourth big photo in the center of the Home page which says Play Chess. Once you are in Chess mode, you will be asked to enter the username of the player who you want to play with. To send a challenge invite to the player, just type his/her username in the search bar and tap “Search”. Same with Chess Roll, you can only search for players who are already registered and are currently online.