There are two common ways to sew up stuffed animal openings – whipstitch and ladder stitch.
Whipstitch is super easy – it’s what I do with the youngest stitchers, as young as four. Here’s a video showing how to whipstitch. The drawback is that the stitching is visible.
Ladder stitch is preferable because it’s totally invisible. It isn’t exactly tricky, but it does require a little more skill with the needle than the whipstitch method. So if you’ve never done much handwork, try the whipstitch a few times – until you get comfortable with it. Then give this a try. It really is invisible and once you get the hang of it it doesn’t take any longer than whipstitching the opening closed.
Note – There’s an excellent question in the comments about when to iron. I iron after I turn it right side out and poke out the corners – but before I stuff it. It’s really easy to turn those raw edges in and press them nicely while the softie is still flat.
Ladder stitch is perfect for stitching up those stuffing holes. Give it a try. 🙂