Pin down the whole bird, including the tiny triangle that is the beak, onto your background fabric. I'm using a blanket-stitch setting, but you can also use a wide zig-zag, buttonhole stitch, even a satin-stitch to do machine applique. I've also chosen a black thread, to complement the folk art look but use whatever color best suits you and your bird.
Begin at the top of the beak and sew down the body of the bird. You will need to have the needle down to pivot around the corners on the tail. If you have a needle down setting it's helpful, if you don't just manually lower the needle each time. When you get back to the top of the beak pivot again. Lower the needle, raise the presser foot, and turn the fabric, before lowering the presser foot again.It may help to use a seam ripper or the point of a pin to hold the fabric flat as you sew down the edges of the beak.Then just add an eye -- I couldn't resist using the "eyelet" setting for that -- and trim your thread ends and you're done.