My last garden was heavy clay (built on a former brickworks!) in the October I dug in compost and broke up the big clumps (some were huge) and mixed in compost so they wouldn’t stick together again, and by the spring I was planting. I only used a small border fork and definitely didn’t go deeper than 20-30cms. Are they wanting to grow veg in it or have shrubs/flowers etc
All the garden was solid clay when I moved in. at the start I dug out two fairly small beds and dumped all that clay (tonnes). I then bought in manure and I add more every year. It worked to give lovely beds, but they are small about 1mx2m. On some of the rest of the garden there are raised beds. I don't need or want more planting areas than I now have. Two small plots are fine for me. For a big area it's not very practical to move clay on a large scale without a digger / a truck.
I think the depth you work to depends on what you want to plant and also drainage. You can't plant shrubs and deeper rooted plants into 15 inches. I can't grow roses anyway, because they drown in winter, but building up a good layer of topsoil and mound planting has worked well for me with many plants. You have to work to your own conditions and depending on just how much clay there is.
It also depends on the kind of 'clay' you have (or the degree of composition). There were Roman potteries close by that took the clay to process. But in my garden it's not the solid stuff you could scoop and make bowls from like the below.
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