They need to be aligned
Well, technically the wheels need to be aligned. This doesn't have much to do with fitting tires and is more of a mechanical maintenance item on the car. It's a good idea to have an alignment done when you buy new tires because poor alignment will make your tires wear out very fast. Since its a new car, if you drive on good roads and don't hit any huge bumps or potholes, you can probably skip getting an alignment on your first tire change. Most people won't get an alignment unless the tires show obvious tell-tale wear patterns, so this is up to you. If your car wants to drift to one side of the road, or you notice that you have to hold the steering wheel off center to drive straight, you probably need an alignment.
They need to be balanced
Normally tires only need to be balanced when they are installed. A properly balanced tire will wear evenly and should remain balanced over its lifetime. The balancing weights can come off, and it is possible for the tire to become unbalanced for other reasons, so its possible to need a re-balance, but this is only done if you feel an obvious vibration. Some tire shops might sell you a "lifetime balance" and they will check them when you come in for a rotation.
They need to be rotated (assuming this was the third point)
This definitely needs to be done at regular intervals. Each tire manufacturer will have a recommended interval to do this, and its important to follow their guidelines if you want your "mileage warranty" to mean anything, and to get the most life out of all four tires. Typical intervals are 4000-6000 miles. Most tire shops will do this for free if you bought the tires there, but you can also do it yourself with the right tools (Jacks, jack stands, torque wrench). There's no way to tell if you need to rotate the tires - you just have to do it on a schedule. If there is an obvious difference between the wear on the front and back tires, you've waited too long to rotate them.