Tiny little stitches with a thinner needle than I generally use for piecing. Trimming is also really important, clip down to the seam line at sharp angles.
You also need a couple of handy "tools" that can be knitting needles or those orange sticks for manicures to help turn the seams and keep the points or curves or whatever crisp. You want something that you can maneuver around but not too sharp so you go through the seams. Nice thing with the flip over technique is you can cut the slit really big/side to side even and get in there for the proper shapes.
My friend that I learned from was a big believer in silk thread for hand stitching down the sides and she used an Ott light both for good color match and to help her see. With my vision issues I find the Ott light necessary for my hand stitching of bindings which is about all I do in terms of handwork, I use a big needle and don't think I could even thread one of her hand stitching needles, probably can't even see a single thickness of that thread any more for that matter!
I had another friend who used to make simply glorious appliqued wall art using the mono-filament clear thread and the smallest zigzag her machine had. At least back then that didn't wash well and didn't iron at all (melts!), but I was in awe of her abilities.