When sewing garments, you'll find that using elastic becomes very common, especially in children's designs. Here are a couple of simple tips that I have found to be helpful and thought you might too.
I like to start by making small marks all along one side of the cut elastic I plan to use. In this instance it is for a waistband. This helps me keep the same side of the elastic up as I thread it through, preventing it from being twisted within the waistband.
Once through, it's time to stitch the 2 ends together.
I always, always, always use a 3-step zig zag stitch here and stitch it back and forth several times. This gives me the peace of mind that it will hold well regardless of being stretched over and over. The zig zag stitch also seems to pull the narrow elastic through my machine easier, where a straight stitch will often bunch up.
Finish your garment per instructions.
Now you're ready to admire your finished item!