This is a trickier part: I suggest going slow with curves. Whenever you stop sewing, finish with your needle in the fabric. By doing this you'll avoid losing a stich or falling out of your alignment when shifting your fabric around.
Hand placement is important: you want your fingers close to the needle head, almost pointing towards it. You'll have to focus on slowly tucking fabric an inch or two at a time as you guide your circular matter along your chosen guide line (you may find pins useful at this point). Sew all the way around, stoping 1.5 inches short of where you started. This will allow you to turn this part inside out.
Do so gently and patiently for best results!