You can use this method for making a hooded shirt from scratch or for reconstructing an existing shirt.
If you are making your own pattern on the fly, I’d suggest finding a hoodie and tracing the hood, making sure to add a seam allowance. You may need to alter the hood to fit the top you want to sew it to- just remember that the bottom edge of the hood should be the same length as the measurement around the neck hole.
Your hood pieces should be sewn together before you start, and the edges finished. You can hem the edge or trim it with contrasting fabric or lace.
You can also line your hood. Cut two pieces of lining fabric the same shape as your hood. Sew the lining together. Then sew the lining to the hood, right sides together. Don’t sew the “neckline” edge of the hood and lining together. Leave that edge open so you can turn the pieces right side out, and then baste along the neckline before sewing the hood to your shirt.