You will need:
One beach towel (mine was from the Target $2.50 dollar spot last summer)
Thread to match your towel (I used aqua blue for this towel, or you could use a contrasting color)
Elastic thread (sold by the elastic, not the thread)
Straps (you can use fabric, ribbon, webbing, or leave the dress strapless)
The first step is to thread your machine with the top thread (not the elastic thread). Then hand wind your bobbin with the elastic thread. This must be hand wound and you will have to do it many times during the dress. You could go ahead and wind 3 or so bobbins before you start.
Once your machine is threaded, you will sew multiple rows straight across your towel. Sew down the longest side of your towel and use your presserfoot as a guide to keep your rows straight. I measured how many inches of shirring I wanted, and then sewed enough rows to meet that length. Once you have sewn all the rows, your towel will look like this.
Take your steam iron and hold it over the rows you just sewed. High steam is key.... if it doesn't work you can spray some water on the fabric and then steam it with your iron. It will shrink up the elastic and shirr the fabric.... this has to be my favorite part. It's like magic! :)
See how tight the fabric is now that you have shirred it?
The top will form a ruffle type thing. This will vary depending on how close you sew your first row to the edge of your towel.
Then, place the right sides of your towel together and sew a seam. Make sure you change out your bobbin to regular thread now.
I would not recommend cutting the towel edges close to the seam as they are anchoring your elastic thread in place. I would iron them flat so the dress will hang nicely.
Add your choice of straps (ribbon, fabric, or webbing) to the desired length and enjoy!
I made a child's version of this dress here.