First make sure that any of the pictures you want to transfer from the phone to the computer are saved as "Photos" and aren't just part of a text discussion.
Next, I turn ON the phone, making sure I'm logged into the phone with the main screen showing. I also make sure the computer is on with the desktop screen showing. I then plug in the cable to the phone, then to the computer. When the phone detects the computer, a popup screen should ask if you "Trust" the computer, you select 'Trust' and the computer should detect the device and can be opened in "This PC". A folder with photos can then be navigated to and opened. Sometimes, the Apple device driver will need to be installed but that happens automatically.
And if one USB port doesn't work perfectly, try another one.
Hope this helps.
Sometimes my pc won't download photos and I have turned it off and back on, turned the phone off and back on and it sometimes works and sometimes doesn't. thanks Rayzerray