It took a while for me to figure out how to delete photos on my new iPhone 6s. It is actually easier than it used to be once you know how to do it.
With the Photos app open, choose Albums > Camera Roll. Press down on an image. The image gets bigger. Don’t let go of the image and swipe up. Options appear at the bottom of your screen, allowing you to copy, mark as a favorite, share, or delete. If you choose delete it asks you again before acting. I found that it sometimes took more than one try to get it to work, but perhaps practice will improve that.