There are 5 steps to the turn. The Approach, the Flip, the Push, the Streamline, and finally the Breakout. Here is a sequence of pictures showing these steps. I used snapshots from another Speedo produced video, with Ryan Lochte swimming. However, the last two pictures are from the Race Club, with a swimmer that I do not know.
1a & 1b) The Approach. When approaching the wall make sure your strokes are full strokes and you hold a strong kick all the way to the turn. Notice a small detail on these two pictures. On 1a you see that at the start of the stroke the head is on the surface, as the final stroke goes through the head dips underwater, notice on 1b how the head is just underwater.
2a & 2b) The Flip. On 2a see how the head is deep by the time the stroke is finished, it is not on the surface! At this point the hands are by the hips, and you push down with them to speed up the turn, and get the hands to the streamline as seen on 2b. The hands will push down until they get to the streamline.
3a & 3b) The push. Notice the toes pointing up through the push.
4a & 4b) Getting off the wall. Here you can see how on freestyle you leave the wall on your back/side. Remember that Ryan Lochte is very powerful so he leaves the wall very much on his back. You can turn on to your side a little sooner than seen on the pictures.
Unseen: The streamline. The streamline starts on the position seen on 4b, staying on this position you start a strong dolphin kick which will keep the body rotating onto its front.
5a & 5b) The Breakout. The breakout is the first stroke, it starts when you are still underwater, as you can see on 5a. You have to time it so that your body breaks the surface as your stroke finishes as seen on 5b.