How to turn off the rotation lock for my iPhone 4?

Going to the home page & double clicking then moving to the right or left does not show a grey button with a lock surrounded by a circular arrow- so what's another way please?

Go to the settings icon. It's the grey clockworky thing. Just press it and go forth from there until you find what you need. It's easy really if you go through the helpful, but somewhat small book that came in the box.