I was taught to use a piece of cheap cheese cloth for the back, sew around the bird the way you want it, then take the Hallmark yarn, (triple cord like), separate the cords, use a large needle with a big eye, fold a small piece of paper with the yarn inside to thread your needle. Then take the needle and pull the yarn thru, side to side, cut the yarn and take the back of the needle to push the yarn in, then draw the second pull thru and continue until you have it stuffed the way you like it. If you have a red cardinal, you could use red yarn, etc.
There is another way where you have a fabric on the back, sew around it, then cut the a hole in the back and stuff it, then sewing the hole shut. I have done both methods and the Hallmark yarn is much easier and is nice and soft.