It's taken Britain a fair amount of time to discover the American writer Annie Baker. But now that we've found her, we must never let her go. She is the real thing, a playwright to cherish.

The National Theatre has imported The Flick (from 2013) and the magisterial John (2015) which has just finished its run in the Dorfman and is an absolute must for anyone who cares about the state of American drama, or the life of theatre in general.

Now HOME in Manchester is showing her second play, Circle Mirror Transformation, written in 2009. It's clearly the work of a younger playwright, lacking some of the complexity and richness of theme that marks John in particular. But it shares with her later plays an astonishing humanity. Baker is a writer who looks hard at people and sees them clearly – but her instinct is to treat them with kindness.

Circle Mirror Transformation depicts the events of a six-week acting course in Vermont, USA. In this production, beautifully designed by Samal Blak to combine the abstract and the real, the scene rises on a community room with red wood walls and turquoise curtains that are drawn back to reveal huge mirrors. A double door and a clock, that shows the precise time each action lasts, dominate centre stage.

In this setting we meet Teresa, James, Schulz and Lauren, amateurs all, who are taking a class run by poised and perfect Marty. It's the type of therapeutic teaching that asks them to reveal something of themselves and learn to be performers by engaging in a series of improvisations and exercises. "Aren't we going to do any real acting," Lauren asks plaintively, explaining that she has taken the course because she wants to land the part of Maria in a school production of West Side Story.

They don't. Instead they get to expose more and more of their inner selves as they fling their bodies into activities where they lie on the floor, trying to count to ten to prove they are "in the moment", or stand in a circle where they mirror and then transform another's action.

Asked to use another class member's life story to make their own monologue, truths they try to hide pour out. When he constantly describes her as "amazing", we would guess that shy, clumsy carpenter Schulz (wonderfully wounded Con O'Neill) was having a brief affair with uptight ex-actress Teresa (Sian Clifford) even if we hadn't seen their fumbling encounters in the breaks between the lessons. In the same way, her growing feelings for James (Anthony Ofoegbu) who just happens to be Marty's husband are shown in her rapturous summary of his life.

The exercises will be familiar to anyone who has ever taken a psychologically-based acting class. They are often very funny, as in the moments when Yasmin Paige perfectly catches all Lauren's hunched teenage embarrassment at having to embody a baseball bat or when Amelia Bullmore's cool Marty struggles to retain control while simultaneously understanding the swirl of emotion that is being released around her.

What is extraordinary is the delicacy and skill with which Baker builds a play out of them. She's often compared to Chekhov, for her empathy, but her dialogue is even more spare and pared back. Nobody really says anything, most conversations are fragmentary, and interrupted, but by the close we know an immense amount about these people and care about their happiness and their sorrows.

The demands on the actors seem like nothing but are immense. They have to show their technique, yet also build a character. Under Bijan Sheibani's clever, sensitive direction, they do so magnificently. The scene where Teresa and James repeat banal words - 'goulash' and 'ak-mak' - and gradually magnetise each other is mesmerising. So is the quiet conclusion with Lauren and Schulz.

It is a lovely play and a deeply rewarding evening.

Circle Mirror Transformation runs at HOME in Manchester until 17 March.