Don't underestimate the talented Mr David Shrigley

When the Turner Prize list was announced this year it was met with mild indifference. With the international art-world darling Tino Sehgal on the list, the outcome seemed almost a foregone conclusion. David Shrigley's inclusion – he was nominated by a judge, Ralph Rugoff, for his show at the Hayward where Rugoff is director – seemed almost an afterthought.

Yet when I checked the official odds at the announcement Ladbrokes gave Shrigley 2/1 odds of winning the award. Not long afterwards Shrigley appeared on the international shortlist for the Fourth Plinth competition and quickly became a favourite. His Really Good, a bronze cast of a hand with an out-of-proportion thumb raised 10 metres high is, he hopes, something that "would make Trafalgar Square, London, the UK and the world a better place".

I meet Shrigley, who is boyish of mien, at the cooperative Glasgow Sculpture Studios where he works. He whisks me upstairs into his space, dominated today by what he fondly refers to as "the man", a pink and very naked robot, a component of his forthcoming Turner Prize exhibition.

"Do you want to see the robot in action? He blinks and pees at random intervals." The man finally urinates (clear water: as Shrigley says "he is well hydrated"), and we settle to talk about his life in Glasgow, a city that, he says, has evolved since 1991 when he graduated with a 2.2 from the Glasgow School of Environmental Art. (I mention the 2.2 as Shrigley continually brings up this grade in interview.) "When I graduated I did not know what I wanted to do next. I did not know you could have a career as an artist. There was an exhibition called Windfall by Douglas Gordon, Christine Borland, among others, who took an unused building down by the Clyde, a bit like the Freeze exhibition, and that seemed exciting.

Shrigley's work was different from that of his peers. Funny was not something that was encouraged. As Penelope Curtis, (director of Tate Britain and on the Turner Prize jury) said, obviously feeling the need to defend Shrigley's inclusion on the Turner Prize list, "just because it's funny, it doesn't mean it's not good."

Deliberately clumsy, and frequently including mistakes and crossings-out, Shrigley's drawings and signs are instantly recognisable and always witty. He points at a sign "Honesty, accuracy, Shrigley", and says "That used to be above my studio door. I like signage and missives." He has pragmatic answers for my questions. "I don't have a manifesto for my body of work. When I am making a work or a drawing I am filling a page and when it is full I am finished. It is just a process." He is a good self-editor, he says, prepared to throw away drawings that don't work, ripping them up into "teeny-weeny" pieces so that they can't be recycled.

Sculpture has appeared more frequently in recent years. An immersion blender, of the sort used to make soup, sits on the floor: "We use them for mixing glazes for the ceramics," he explains, and points at a group of colourful shoes that will be the focus of a forthcoming show in Berlin. The shoes, he says, "are not really shoes, they are representations of shoes" and will be shown with bronze faeces that are presently being cast.

He does his "drawing and thinking" in his flat in Glasgow's West End, "I need to keep the drawings clean. The ceramics I make here create a lot of dust".

He shares his flat with his wife Kim and a miniature schnauzer, Inka. I ask if she will be immortalised, as per his frequently reproduced work of a stuffed terrier carrying a sign reading "I'm dead", and he sighs, "people don't realize that there are rules on taxidermy".

Born in Macclesfield in 1968, Shrigley enjoys living in Glasgow, admitting "I found it exotic when I first arrived, having grown up in Leicester", despite the "truly shocking" weather. "Glasgow is big enough to do what you want to do"; there is a community of artists and an independent music scene, and it's easier to live in than London, he says. "I never go to art openings; I prefer instead to have music as the centre of my social life." When he was younger he played in bands, and he has collaborated with Blur and, more recently, Franz Ferdinand. He also wrote the libretto for Pass the Spoon, a "sort of opera" about cooking. "When I was asked, I thought 'I will work with good people and they will make sure that my contribution is not shit!'"

Despite the breadth and unmistakable popularity of Shrigley's work, he admits "I think a lot of people who like my work don't see it as fine art. They see it as illustration or comic." I ask if this is difficult in relation to other Turner Prize nominees, and he replies, "When I asked Stephen Friedman [Shrigley's gallerist] if he should accept the nomination, he said it would be good for business, so I did. I have had the Hayward show ... My attitude to work is that unless you say yes, the moment will pass."

But after all there is an overarching self-critic in Shrigley: "I focus on the process and I don't think of the end result, but of course there is quality control, as I want the work to be engaging and entertaining."

And then, just when I think he is being too earnest, out comes the Shrigley wit again, "My criteria for making any artwork is that it is not shit."

The Turner Prize is at Ebrington in Derry-Londonderry as part of UK City of Culture 2013 (cityofculture2013.com) 23 October to 5 January 2014; the Fourth Plinth Shortlist exhibition, St-Martin-in-the-Fields, London W1 (stmartin-in-the-fields.org) to 17 November