To resign a game, you need to open the game that you wish to resign and then press the Hamburger Icon (three white horizontal lines).
Tap the "Resign" option or the icon with "White Flag"
Another rule is, if your opponent does not make a move soon, then the game will be automatically resigned for you.
The auto-resign times are as follow:
Random opponent games - 5 days
Non-random opponent games - 11 days
Games that are inactive past these time limits will be auto-resigned by the game server. For Random opponent games, auto-resignation will occur on the 6th day following the last game action. For Non-random opponent games, auto-resignation will occur on the 12th day following the last game action.