Hi Debbie, it depends if you want your stitching to be visible.
You could sew round the middle of the elastic all the way round your skirt using a zig zag stitch, to secure it in the casing.
If you want it to be less visible, you could also stitch in the ditch down the seam lines at the side and/or back of your skirt.
Another option would be to not sew it in a casing. Once you have sewn both ends of your elastic together, pin it around the top of your skirt (to the wrong side of your fabric), stretching the elastic as you go. Sew with a zig zag stitch or use an overlocker really close to the outside edge. Once attached you can then fold it over and sew it down, this time you need to sew it close to the raw edge, not the folded edge. This gives a slightly different finish to the waistband.
If the elastic is not comfortable round your waist, you can always go for something wider. 20-25mm will be fine for children's clothes. It's all personal preference!