Managing space on iPhone 5s / photos and videos

How do you delete photos and videos from your iPhone after you have synced them to your computer? I need to free up space on my iPhone 5s and I believe the photos and videos are taking up most of the 16GB memory. I have synced them to my computer and they are showing up in my photos file on the computer. Now I need to delete them from my iPhone and iCloud. Can someone help me with this one?

Also, I notice some photos that I took on a regular camera and downloaded to my computer in a photo file are now showing up on my iPhone? I think I want this to be a one way sync from iPhone to computer only, how can set that up?