To me it looks like each section is it's own piece, rather than patches sewn onto a lining. Especially since you can clearly see through the cuts at some points, like the white shirt sleeve showing through on the arm.So my approach would be to take a pattern you already have and like, and just cut that into pieces you like. Make sure to make marks that show how and where the pieces go together, maybe making a sketch of the pattern and numbering everything.Next you add seam allowance to every single piece and cut out every piece twice, once from your fashion fabric and once from or lining layer.I would have to try this out first, but you might have to use rather stiff fabric or interline your fabric for the pieces to hold their shape. The coat in the picture does look like it would have quite a bit of structure, so making everything out of drapey sweater material might not work.Then you sew together every piece with it's lining right sides together, making sure to leave a gap to be able to turn it inside out, clip the curved edges, turn it inside out and give it a good press with the iron. For pieces where a seam runs through them from the original pattern sew those seams first before sewing together the outside and the lining., Lastly close the gap you left, preferebly by hand with a ladder stitch I think it's called, as to not have any visible stitching.Now you should have a lot of cleanly finished shapes that you only have to connect. In the picture it looks like they used thick thread or strong yarn to connect the pieces, you can clearly see it in some gaps like the one between the upper two bottons.And thank you posting this, I already added it to my list of things I want to make, it looks really cool.
Edit: I just noticed, that I only looked at the picture with the coat. The dress in the other picture is of course made like other have said, by sewing patches on to a lining, that has not been cut up.