It's not about making the image smaller.
Websites are best designed in elements. This means creating a wireframe with all your divs and classes and the content included. You then style each element on the page, testing on different devices as you go. For example, you may want to begin with the menu function - pull in the pages and style for widescreen, tablet and mobile. Test in landscape and portrait and make sure your touch elements meet the Google accessibility guidelines. Test different versions - with and without the hamburger, dropdowns, flyouts and animations.
Don't fall into the trap of designing the site using an image editor. You need to be designing on a dummy site so you can see how each element works.