You have the right idea. Make your purse first, turning it right side out. Then make the lining with the same pattern - however, be sure to leave a small opening in the bottom of the lining to pull the purse through.
When the lining is all sewed up, slide the outside of your purse inside it. You'll now have the right side of the lining and the right side of your purse facing each other. Sew the lining around the top of the purse. When done, pull the purse through the little opening in the bottom of the lining. Turn the raw edges of the hole in and stitch it shut. Push the lining inside the purse and it's done!