To delete photos from your phone, go to your camera or photos app, once you tap on one of the photos you should see the trash can icon in the bottom right.
Copying photos from your computer to your iPhone, you have to tell iTunes what folder you want to sync with your phone. This will create another album that will hold pictures FROM your computer on your iPhone.
To get pictures OFF your phone and onto your computer, go to My Computer, you should see your iPhone, double click on it, and follow the folders until you see something like Apple 100. All your pictures and videos will be in there.