Sandpat, the pointy points are done by manipulating the absolute point with the tip of your needle---whether needle turn or freezer paper method.
You'll pinch with your thumb nail to hold the excess fabric back, place the tip of your needle right at the end (after tucking excess fab underneath) and go straight down through the fabric. I leave my thumbnail there and go immediately to the next stitch and then make sure everything is tucked in. I hope that's clear.