Karen Dunbar didn't know much about Samuel Beckett's work before the Tron Theatre's artistic director Andy Arnold asked her to play Winnie in Happy Days, which opens next week as part of the theatre's Mayfesto season.

Now, however, she's something of an expert on a play which at first glance looks like one of the oddest ever written.

"It's pretty left field," says Dunbar, sitting in an upstairs meeting room at the Tron, all wrapped up in a warm coat and woolly hat as she sucks on an E-cigarette attached to a small cannister with the word 'zen' on the side. "I can't say I came to it as a big Beckett fan. Nah. I just said, Samuel Beckett He's a writer. Is he Irish? No, he's American. No, wait. So that would've been my answer on Who Wants to be A Millionaire? Now, of course, I could tell you what colour flannel he prefers wearing. I do enjoy studying, studying for a cause. I actually like reading random pish about nothing, anyway, so it's been really enjoyable, not only looking at Happy Days, but looking into his other work and to the man himself, and finding out about his influences and who he's influenced, I feel very much educated in it now."

Written between 1960 and 1962 Happy Days finds Winnie buried up to her waist in sand as she chirrups her way through her daily routine while her husband Willie hides behind his paper, barely acknowledging her beyond the odd distracted exchange. By the second act, Winnie is buried up to her neck, but on she goes, however fragile her eternal optimism remains.

When Dunbar first read Happy Days, she did so with "one raised eyebrow through the bulk of it, but even from the first read I knew it was brilliant. I'm thinking I'm no' quite sure why yet, there are bits I don't understand, the intonation I cannae imagine, there are references I have no idea about, but even though at that point it was way over my head I could tell it was high quality stuff. Now, having really explored it, I go away and can get too deep sometimes over each syllable."

Dunbar has been learning Beckett's script since January, working on two pages a day and writing her lines out by hand. This is something she always does when rehearsing a play.

"It puts it into a different space for me," she says, "seeing it in my own hand-writing and having to concentrate on writing it out and punctuating it. It makes it a wee bit more tangible for me."

Dunbar now has a very tangible seventy-six pages of Happy Days penned in her own hand, and by the time she began rehearsals had ninety-five per cent of it memorised.

"Usually I would just learn lines on the go, but I knew with something this size I wanted to be really prepared. See to come in knowing the lines to the degree that I do? What a joy."

The last time Dunbar put herself on the line in such a way was in 2008, when she was about to revive her solo tour de force in A Drunk Woman Looks at the Thistle, novelist Denise Mina's female-fronted twenty-first century reboot of poet Hugh MacDiarmid's sozzled meditation on the Scottish psyche. Since then, Dunbar's theatrical career has combined stand-up, pantomime and TV comedy shows alongside more straight-up theatre with low-key regularity.

With the National Theatre of Scotland, Dunbar played the abused Rose in a revival of Quebecois writer Michel Tremblay's all-female tragi-comedy, The Guid Sisters, translated into Scots. More recently, she played Bardolph and Sir Richard Vernon in Phyllida Lloyd's all-female production of Shakespeare's Henry IV at the Donmar in London.

For Arnold, who as well as directing Happy Days will also be applying his own performing talents to the play's infinitely less vocal role of Willie, casting Dunbar was a no-brainer.

"I think Karen's an amazing performer," Arnold says, "and she's perfect for Winnie. You have to remember that Beckett was a big fan of Laurel and Hardy and Charlie Chaplin, and that really comes through in his work. But there's a depth to that sort of comedy which Karen has as well."

Dunbar was doing Henry IV when Arnold approached her.

"I remember telling Phyllida Lloyd," she says, "and she's a lovely lady, and she's very honest. She told me she thought I'd be great at it, which was lovely to hear."

Now she's immersed in all seventy-six hand-written pages of the play, Dunbar likes to describe Winnie as "a cock-eyed optimist, just because of South Pacific, but she is an eternal optimist. Not even in a denial kind of way, but I think she is genuinely cheered by what she tells herself, and she's cheered for the fleeting moment that she says it. That's enough to give her a wee boost."

With comic turns from Max Wall to ex Comic Strip double act Rik Mayall and Adrian Edmondson having appeared in Beckett's work, this lightness in the play is ideal material for Dunbar to have fun with.

"Definitely," she says, "and hopefully that's gonnae be an asset for me, being able to bring the humour into it. There's such darkness in it. There's such sadness, so I feel like I've got a bit of responsibility as well, to make sure it's the right level of humour, that it doesn't become a caricature, but that it's believable, because I want it to be the same when it comes to the dark stuff. I think it's hard sometimes for somebody that's known for comedy when they do a serious role. You say a line like 'all my family are dead' and the audience are waiting for a laugh.

"That can be a bit of a challenge for me, not, hopefully, in trying to portray the seriousness, but in trying to step a wee bit away from what people know me as. It was great doing Shakespeare in London, because there's no frame of reference there for audiences with what I've done before. So I can play a funny part and a serious part with hopefully the same sincerity.

"Comedy's a huge deflector," Dunbar says, pointing to her portrayal of Rose in The Guid Sisters, "and it's a great relief sometimes as well. I quote it often, but what is laughter but making the unbearable bearable. The majority of comedians, there's always a sadness underneath. It's why the comic character comes out of a person in the first place, as a balm for the pain.

"Oh," she says, without missing a beat, "that was awfully deep."

Happy Days, Tron Theatre, Glasgow, May 15-23.

www.tron.co.uk