Begin by cutting out 2 matching owlish shaped pieces. Mine is about 6" at the widest point, and 6" from the tip of the ear to the bottom. Cut several templates of paper until you are happy with the shape.
Choose a contrasting fabric, cut and iron a piece of fusible/iron-on web to it. Then cut the contrasting fabric into a shape similar to the one below. (I always skip this step, and sew directly)
Remove the paper backing and iron on to one of the main body pieces.
Stitch around the edge of the smaller front piece using a decorative embroidery stitch. I used the banket stitch for this one.
At this point I sew the main front and back pieces together (right sides facing each other) by hand or by machine, leaving the bottom open for stuffing. Clip the v point between the ears, and where the ears meet the body. Also make a few clips around the round part of the body. This will help the body lay right when you turn it. Be careful not to clip the seam. Turn inside out.
Once the owl is stuffed, turn in about 1/2 inch and sew closed.
This is where I add the beak and eyes. I like having the body done when I add details, though this step can be done befor the body is constructed.