Thanks to recent improvements, it is really easy to start playing chess games through Lichess using screenreader. The first thing you need to do is to press “Enable blind mode” button, which should be one of first elements you encounter on the site. It is not really possible to play games without blind mode turned on.
If blind mode is on, you are offered textual description of moves and you are presented with labelled buttons. Now it is really easy – pick a player or just choose to play against computer and fun begins. During the game there is a heading called “Textual representation” and following this heading are following information: