Ensure the screen/phone is unlocked, then pull the notification shade down, tap where it says USB Charging, and change it to File Transfer. With the Marshmallow update, the default USB mode is charge only.
It's not a button, it's a notification. See if this helps:
You may need to unplug the USB cable and then plug it back in again (or try a different port).
Being able to copy your pictures to your home computer to share with friends and family, and keep a backup is important JENGA747. As tikibar1 has stated the correct steps to do this it is concerning that you do not see that option available. Let's get this figured out so you can move those photos over. What do you see when you pull down the notification bar when the phone is plugged into the computer? Is this a Windows computer or a Mac?
Can you send us a screenshot of what you see. You can take a screenshot by pressing the home and power buttons simultaneously.
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