When everything is stitched together, grade and clip the seam. Grading is simply cutting off half of the seam allowance from one of the fabrics so that the seam allowance is not bulky. Clipping is cutting triangle shaped pieces with the point coming close to the seam. This reduces the bulk in any curved seam.
Understitching will help the collar lay right. From the right side of the under collar, I stitch close to the seam, stitching the seam allowance to the undercollar. I press with my fingers as I go. Getting a presser foot into the curve of the collar is a trick. You need to use your smallest presser foot. I used my freemotion embroidery foot. Not ideal because I have to feed the fabric myself, but it is the smallest foot I have and I can get into the curve with it. Better than stitching by hand for me.
Press the seam allowance under the neck edge of the collar and the under collar as shown here: