This first set of felt puzzles is made by sewing or gluing a picture onto a felt square, and cutting it into pieces. My pictures are sewn on, but you could definitely use fabric glue. Try to make the picture or shape fill as much of the square as possible, to make the puzzle easier for kids.
This felt snowman puzzle was even easier to make. It only took about 5 minutes. I just cut the snowman and clothing shapes out of felt. The pieces stick together enough to make a snowman, but easily come apart to change it up! You could also use this idea to do a “paper” doll.