This process is super easy. The pictures describe the process for making the ruffled/tiered version of the skirt with modifications to make a non-tiered version written at the end. The good news is that you only need to know how to sew straight lines for any of these!
You will need:
Roughly 1/2 yard of fabric. (More for sizes larger than toddler/pre-schooler)
Elastic- I like 1" or 3/4" for waistband, cut to the waist size of your kid.
Sewing machine, pins, scissors/rotary cutter, all the usual bobbles of sewing.
And away we go:
1. Cut the fabric into two strips. One roughly 36 wide and 9 inches long and the other long enough to make the skirt the length you desire and as wide as the fabric selvedge to selvedge. (I make the bottom bit 8 inches for my 5 year old and 6 inches for my 3 year old.)
2. Sew up the two bits into loops and pink the raw edges.
3. Iron the seams open and fold over roughly 1.5 inches on the short/top bit to make the casing and roughly 1 inch on the bottom/long bit to make a bottom hem. Press these folds for ease of sewing.
4. Zig-Zag stitch around the tubes making sure to catch the raw edges in the stitch. This keeps the hem/casing from fraying while making the process easy.
5. Around the casing on the short/top tube run two lines of straight stitching: one right next to the zig-zag and one close to the top of the casing. (Note: this step is optional, it is not integral to making a working skirt, but I feel it does a nice job of keeping the elastic neat.)
6. Around the un-hemmed edge of the longer/bottom tier run a line of straight stitching with your machine set to the longest stitch length possible. Now you should be able to grab on of the "tails" and pull creating a ruffle.
7. Pin the ruffled layer (right sides together, wrong sides out) to the top layer. For this step just keep working the ruffle until it fits nicely and looks the way you want it to look. The only important part is to line up the seams in the tubes.
8. Sew around the tube attaching the two tiers and use your seam rippers to remove the long stitches you used to make the ruffle if they show too much.
9. Here you can use your pinking shears to trim the raw edges, overlock/ziz-zag them or, as I like to do, you can iron that hem up towards the waist then top stitch around the skirt. This keeps the fraying in check and, to me anyway, gives the skirt a nice finished look.
10. Using seam rippers open up the inner seam on the casing and run your elastic through. Sew of the elastic and Viola! Twirly skirt.
To make a similar skirt, but without the tiers/ruffle, just cut a rectangle as long as you want the skirt (measure your kid from waist to desired length and add 3-4 inches). Sew the single tube, pink the raw edges and press the seam open. Fold over your 1.5 inch bit for a casing on one end and the 1 inch bit for the bottom hem on the other end. (Like steps 2&3 only on a single tube.) Zig-zag those fold and add the waistband sewing if desired. (Like steps 4&5) Pop your elastic through (like step 10) and there is another, even easier variant on the skirt that looks like this.
Obviously you can make more tiers, mix and match fabrics (two fat quarters make for cute layered ones), play with the length...whatever you like.