If you were re-upholstering your sofa - as opposed to making loose covers - then most pieces would be stapled directly to the frame. This would necessitate removing the back cover of the sofa and pulling fabric ends through to get them taut, then stapling.
However when you make loose covers, you stitch the pieces together then slip the cover over, like putting a dress on a sofa. So you would need to join seams conventionally for the pieces, using techniques such as clipping on curves to allow the fabric to conform to the required shape.
In either case, you would make the loose cushion covers individually, fit them to the seat / back cushion and fit either a zipper or hand-stitch them shut. I tend to hand-stitch them and simply unpick these hand stitches if the cover ever needs laundering.
You could try to sew directly onto the existing fabric but the stitch lines will always be a weak point and prone to parting under stress, which is a waste of your time and talent, so I'd recommend actually making the lengths of patchwork you need.
I tend to make up all but the bottom half of the sofa back, slip the cover over the sofa, then go round with a staple gun at the back, and the back inside of the seat where the frame can be felt, and underneath the sofa, stapling up any excess to the frame.
You can get loads of articles on machine patchwork and also books - raid your local library before the Condems shut it down.
But if you haven't done this before bear in mind it's a tiring task - why not try out a dining chair pad first?