I use 3/8" plush-back picot elastic. The sample elastic is not plush-back but it will work for this series of photos. 1. Pre-stretch the elastic a few times and then align the straight, non-picot edge of the elastic with the raw edge of the fabric.

2. Attach the elastic to the fabric, sewing next to the picot edge of the elastic with a narrow zig-zag stitch. (The elastic may stretch out during this step but steam or a trip through the laundry will pop it back into shape.)

3. Turn to the back and trim close to the zigzag stitching. I use my duckbill scissors for this. It doesn't have to be especially neat as this edge will not show on the finished item.

4. Fold the elastic to the wrong side so the picot edge peeks out from the right side. Stitch on the right side using a 3-step zigzag stitch. (The brown layer of fabric is here only so you can see the picot edge.)

5. This is what the 3-step zigzag stitch looks like on my machine.

6. This is the wrong side of the last stitching. If your thread matches your elastic, it's nearly invisible. The 3-step zigzag stitching can be anywhere between the 2 edges of the elastic. Ideally, mine would be overlapping the straight edge of the elastic to hold it down in a more finished-looking manner (which means I needed to sew more to the left in Step 4), but I was making a fast sample and wasn't paying close enough attention. ;-) I'll try to remember to update this photo when I have a better sample.

I've used other methods to attach the elastic, including trying out my serger's elasticator foot and also my coverstitch machine. (See photos here). In my opinion, the method above using only the sewing machine is the best for durability and comfort in the normal course of lingerie wear. The other methods work fine initially, but the extra thread and stitches cause elastic fatigue and result in more popped stitches. The panties I sewed that way just didn't hold up as long as those sewn from the same fabric but using only the sewing machine.

By the way, I sew leg and waist elastic on in the round. I overlap the cut edges of the elastic as shown below, and then zigzag them together. I think it creates less bulk than a RS-together seam with the allowances pressed back. The overlap goes at the outside of the leg and the back waist.

I sew like this: