The solo variant sets the player against an AI opponent called The Dead Ranger. Your goal is to kill him, if you play on easy. For increased difficulty, you will have to kill the Ranger, control buildings and eliminate undead outlaws. You play as the law, and begin the game with a number of outlaw meeples. The Dead Ranger has his own outlaws too. Placing outlaws will trigger duels between the two sides. If you lose, you place your outlaw in the graveyard, gain a bullet, and add an undead. If you win, you remove the undead outlaw and replace it with a card. By succeeding in your 'intimidate' actions, and killing the undead outlaws, you can eventually take out the Dead Ranger.
You may want to read more about the game in the rulebook posted on the campaign page.