My little girl loves purses. If I bought her a purse every time she said, "That's cute!" I'd go broke. Instead, I taught her how to make her own bag, and now she happily walks around with her own handmade purse.
First cut your felt as shown. Your child can do this, but for this particular project I cut it out for my daughter. The smallest piece is extra and can be used for another project later. (Like a monster felt board!)
Now line up your smaller piece on top of your bigger piece. (It doesn't matter if it's perfect, because felt is very forgiving. That's why I like using felt for crafting with young kids.)
You can sew the bag with a whip stitch, where the thread goes around the edge of the bag, or with a running stitch where the needle goes up and down. As you can see, our project switched back and forth between the two kinds of stitches.