In short, rotating your tires will extend the life of your vehicle tires.
No matter how well the alignment is, it will never be perfect because of the forces from turning and if your vehicle is front or rear wheel drive.
Not all vehicles require the same rotation sequence. You will have to look in the owners manual to learn the best pattern for your specific vehicle. Another thing to keep in mind is if your tires are directional, meaning that they are designed to run on the road in one direction only, there are additional challenges in rotating so your cost will be more.
So when should you rotate your tires? Again you will have to refer to your owners manual but when in doubt just plan to do it every time you have your oil changed. The most critical time is during the first 10,000 miles on the car.