The pattern features underarm gussets. The instructions call for inserting the gussets in the standard way. Gertie, of Gertie's New Blog for Better Sewing, has a lovely tutorial about how to do it. You should read it! It's really great.
I tried inserting gussets this way when I was sewing the muslin of the bodice. Sadly, I am really bad at stitching corners using the stitch-and-pivot approach-- I just don't have the precision to pull it off. The results looked like this:
Yep, I was 0 for 4 at well-executed gusset insertion. I'm sorry, Gertie!!! It's not your or your tutorial's fault!
So, I devised a way to insert gussets which would play to my strength, stitching tricky corners with lapped seams. I now provide the following tutorial in case you want to do it yourself. I don't know if this method gives better results overall, or how durable it is in the long term. But, it was easier for me to pull off, so here you go.
1. Prepare the Gusset Pieces
Transfer the marking of the point of the gusset from the pattern piece onto all of the gusset pieces.
Turn under the seam allowances and press them to the wrong side of the fabric. I kept the thread marking showing the point even after the pressing was complete to make the point easier to see in the following steps.
2. Prepare the Bodice Pieces
On the wrong side of the fabric, interface the slash into which the gusset will be inserted. I used three strips of silk organza, two parallel to the slash, and then one at the point, perpendicular to the slash.
Pin the gusset piece to the right side of the bodice piece so that the gusset piece covers the lines of stitching holding the interfacing to the bodice pieces. That description may be confusing, but the picture should convey what I'm trying to say. The key points are that you pin the gusset piece on top of the right side of the bodice piece, and you don't want any of your previous stitching to show.
I hope this tutorial was helpful, and if any parts were confusing, or any of the pictures were difficult to interpret, let me know in the comments and I will fix it!