How to save anchor points in photoshop?

Once you've made your paths with the Pen tool, go into the Paths panel, and you should see a Work Path. If you drag that Work Path down to the Create New Path button, it will make a path called Path 1 that will be saved in your PSD file.

Refer to this screenshot: Drag the "Work Path" to the "Create New Path" button to save a path.