Sewing Room Motifsa Cross Stitch Pattern by Tiny Modernist

This is about the Sewing Room Motifs pattern, which shows the cross stitch project on the lid of a sewing box. I wouldn't have any idea how to do that part. Has anyone here ever finished a cross stitch on the top of an object like this? If yes, what steps did you take to do it?

I would like a list of floss #’s this goes to. It looks like its just the pattern, not a kit. Would like #’s so I can order if I don't have. Thx