The first scene does a great job of establishing Joan's character. Her charm, courage, and faith are on full display as she sways Robert and his soldiers to her side. The scene also establishes the generally unstately state of France. By the end of it we've got a good idea of who our protagonist is and the world she lives in. The stage is set for her to sally forth and kick some English butt.
Once Joan wins over Charles and gets control of the army, she can really get down to business. Her goals aren't small. She wants to raise the siege at Orleans, crown Charles at Rheims Cathedral, and expel the English out of France for good. The main conflict of the play is crystal clear.
In Scene Four, we see the Earl of Warwick and the Chaplain de Stogumber forming plans to take Joan down. They enlist the help of Cauchon, the Bishop of Beauvais, who agrees to try her for heresy. By the end of this scene, we know better than Joan the barriers that are standing in her way.
After Charles gets crowned at Rheims, Joan's buddies want to sit back and relax. Joan, however, demands they get off their lazy butts and keep the fight going. The English aren't all gone. Paris isn't under French control. Tempers flare when her allies refuse to help her and accuse her of being prideful.
Joan's friends warn her that if she continues the fight and gets captured, they won't lift a finger to help her escape. Perhaps foolishly, perhaps bravely, she swears to trust in her voices and continue the fight without them.
The action of the play begins to resolve as the captured Joan is convicted of heresy and is burnt at the stake.
Shaw ends the play with a dream sequence. We learn that, after Joan was executed, her name was cleared and she was made a saint. A bunch of characters, show up and tell Joan they're sorry that they dissed her back in the day. However, when Joan asks them if she should come back to Earth, they all freak out and leave. Joan ends the play by asking God if the world will ever be ready for saints.