Whenever I think unhappily about Alec Baldwin, the way you do when you feel ashamed of knowing too much about a celebrity – whenever I think about his nasty divorce; the horrible voicemail message he left for his daughter Ireland in 2007; the time he fought with a photographer in New York – I remember his performance in one of my favourite old Saturday Night Live skits.

The year is 1993, and Baldwin is at the peak of his dreamy youthful handsomeness. He plays a soap opera actor who claims to have done extensive research to prepare for his part as Dr Dirk Johanson in the ludicrously over-the-top show Doctors, Nurses and Patients, but is unable to pronounce even the simplest medical term correctly.

"Anal canal" comes out as "anal CAY-nal". "We've got the results of your ur-INE test," Johanson declares to a patient, played by Phil Hartman. "It might be the Big C – canker."

You can forgive an actor an awful lot when he can produce something so sublimely deadpan, and then, in Baldwin's particular case, eventually go on to play the great Jack Donaghy on 30 Rock, his dark eyes glinting with anarchic, Machiavellian intelligence; and then to out-dumb President Donald Trump on the current season of Saturday Night Live. So how are we meant to think about this person, whom we know but of course do not know?

It is in this spirit of trepidation mitigated by appreciation that you approach Nevertheless, Baldwin's latest book, a memoir, published in Australia by HarperCollins. (He's also the author of A Promise to Ourselves, about his custody battle over Ireland.)

"I'm not actually writing this book to discuss my work, my opinions or my life," Baldwin declares right off the bat and soon adds, "I'm writing it because I was paid to write it."

After that start, you feel the needle on your Baldwin-appreciation meter trending downward. But to his surprise (and ours) he pulls himself together and delivers a thorough and sophisticated effort to answer an interesting question: how did an indifferently raised, self-flagellating kid from a just-making-ends-meet, desultorily functioning Long Island family, in Massapequa, turn into Alec Baldwin, gifted actor, familiar public figure, impressively thoughtful person, notorious pugilist?

Unexpectedly moving

The passages about his childhood – his mother overwhelmed, depressed, lying in bed surrounded by laundry; his father working at a school; six siblings fighting for space and resources in a two-bedroom house, their parents unable to afford even a washing machine – are beautifully written and unexpectedly moving.

"Six pieces of driftwood," Baldwin writes of himself and his siblings, "just bobbing through our neighbourhood, without a current to carry us in any particular direction, passing time, trying to pass our classes, avoiding trouble, courting trouble, scoring points, telling jokes, drinking, smoking, always mindful of how little we had."

He never intended to be an actor but fell into the job when, as a student at George Washington University, he spontaneously decided to audition for the New York University theatre program while visiting the city. He got a spot despite having no experience, transferred out of George Washington and then had an existential crisis.

Why hadn't he continued with his plans of going to law school? "Why was I spending hours at the Lee Strasberg Institute weeping or directing scenes wherein we staged our dreams or shouting into a corner at some unseen source of my anxieties?"

But then he spent two years on an actual soap opera, moved to Hollywood, moved back to New York, and saw his career rise and then fall and then rise again. His current film, The Boss Baby, in which he voices the character of a tyrannical infant, is No 1 at the American box office. People cannot get enough of his portrayal of Trump, with its perfectly pitched vapidity laced with self-regard.

Nevertheless, whose title comes from a dirty joke that Baldwin heard from British actor Michael Gambon, is full of unexpectedly sharp descriptions.

Of Mary-Louise Parker, his off-Broadway co-star in the theatre version of Prelude to a Kiss, he writes: "With her big eyes and lanky frame, you weren't sure if she was a ballet dancer or a murderer." Harrison Ford, who replaced him as Tom Clancy's character Jack Ryan after The Hunt for Red October, is "a little man, short, scrawny and wiry, whose soft voice sounds as if it's coming from behind a door".

He is tough on himself. Writing about The Cooler, a small film he made in 2003, when his popularity was not at an all-time high, he says, "When I read the script and got to the page where my character kicks a pregnant woman in the stomach, I asked my agent, 'Don't I have enough troubles?'"

Baldwin writes with great knowledge about old films, the art of acting, what he has learned from other actors, and about the differences among television, film and theatre. He also takes the opportunity to settle old scores.

It appears that the book itself has given rise to some new ones. "The editors at HarperCollins were, I imagine, too busy to do a proper and forensic edit of the material," he wrote recently in a Facebook update devoted to post-publication corrections and amendments.

He says that he had no ghostwriter or collaborator for this book. That is impressive, because he's a highly literate and fluent writer, but it also means that his authorial discipline can abandon him. He has a bit of trouble with transitions.

Breathtaking contrast

In the worst example, he's talking admiringly about actor Christopher Reeve, who was president of the Creative Coalition, an organisation for politically involved actors like Baldwin. One moment Baldwin is standing next to Reeve at the group's 1995 retreat and all is well.

And then: "Two weeks later he broke his neck and was paralysed," Baldwin writes. "Soon after that, I was elected TCC president."

Baldwin expresses love for his second wife, Hilaria, and his four children, and seems to have found a new peace after a lifetime of battling his demons. "I want to end this book contemplating happiness and renewal," he says.

The most recent time he hosted Saturday Night Live, in February (it was his 17th time, a record), showed that he had weathered one of the hardest things anyone can face: how to square who you are now with who you used to be. During the opening monologue, the camera panned to a photograph of Baldwin in 1990, when he first hosted the show. The contrast was so breathtaking that the audience gasped.

"I can't believe that was you!" young cast member Pete Davidson exclaimed. "You were so handsome!"

They traded personal-appearance insults for a bit, with Davidson marvelling at the ravages of time. "At what point when you get older does your whole head, like, expand?" he asked. "Does that happen to everyone? Is it going to happen to me?"

"Yes, Pete," Baldwin responded, "and along the way if you're lucky you'll have an entire career."