You need modelling clay. There are all sorts, honestly the easiest is air dry clay. I used this in white, it also comes in terracotta.
You simple knead it so its lovely and soft and roll it out with a rolling pin just like icing. It's a good idea to use non stick baking paper or something on your surface. About half a centimetre is a good thickness.
I covered my semi rolled out clay in lace and rolled over that to create a lacy impression. Then simply used biscuit cutters to cut out my shapes. Then I used a knitting needle to create a hole in each for hanging later.
Lay them flat to dry and turn them after a few hours and press them gently. I find they can warp slightly as they dry and press them flat a few times.
When dry add ribbon or thread to hang them by. Keep what you would like to hang them with in mind when you make the holes so they are big enough.
As you roll them out you will need to gather up your left overs, knead and re roll to use it all up. One pack makes quite a few. A tiny amount of food colouring can be worked into this clay, I made some pale blue. It takes a lot of kneading to get the colour blended and you need gloves!
Once dry they look lovely and there is no limit to what you could do. I have a larger deer cutter so I think I might make some deer!
This would be a lovely craft fro the kids, it isn't messy (unless you add colour) and the results are really good.
We enjoyed our first evening of Christmas lights last night! Lovely.