Starvation is the point where your hunger levels are so bad, you start to take damage to your health, so simply run around, doing what you normally do and let your hunger level run down. When you start taking damage, eat some rotten flesh and the achievement is yours. It is important to note that your hunger levels do not deplete if you are inactive, so you cannot stand still and wait for hunger to kick in.
It is wise to have some normal food, such as steak, to hand as well, as rotten flesh can give you food poisoning, which could do further harm.
The easiest way I found to get rotten flesh was to run into a cave armed with bow & arrow, as zombies only spawn at night. You could also find some by building a simple shack in the middle of no where with a bed in it, wait till night time and then sleep till morning. Any monsters that will spawn at night will be cooked in the daylight, leaving behind their drops (apart from creepers and spiders)