Blackout curtains are hung on rods, similar to any other type of curtain you might buy. However, to help block out light effectively, you should hang the curtain rod at least 4 inches above the top of your window so that light doesn't shine over the top of your curtains. Otherwise, even if the curtains themselves are great at blocking out light, they will still let light in.
Make sure you also pick the right kind of rod for the type of curtains you install — generally, grommet-style curtains require wider curtain rods that are often very ornate and meant to be displayed.