This approach is known as "multi-screen site". Some of its strategies include:
Liquid or fluid layout: Defining all container widths in terms of percentages of the browser viewport, so that they expand and contract as the browser window changes size.
Media queries: Invoking different style sheets based on the capabilities of the display being used, such as size, resolution, aspect ratio, and color depth.
Fluid images: Setting images to occupy at most the maximum display width.