Sounds like the manual transmission might as well be from another planet in the US. As previously noted, there are many ways to skin a cat. High performance or advanced drivers will always use a manual gearbox in a different fashion to the ordinary driver. It is for the former that the heel and toe technique will be important. If you are the latter type of driver, you just won't be interested.
The simple driver is advised to use his brakes to slow down the vehicle to the desired speed, prior to engaging the correct lower gear for his new, reduced, road speed. There are many flaws in this approach, but it is appropriate for a simple driver. It does not matter whether that involves going from 5th to 2nd without stopping at gears in between, so long as gear ration is matched to road speed.
The advanced driver, as he reduces his speed using the brakes, will shift down through the box. This involves the heal and toe technique. With the clutch in, heal of right foot on brake pedal, toe on accelerator (or is it the other way round?), he blips the throttle to bring the engine speed up, while maintaining constant brake pedal pressure. As the clutch comes out, the engine speed should be perfectly matched to brake speed to avoid any sudden change in the balance of the car caused by engine compression. Of course, engine compression contributes to the decelerative effort, but this method ensures that it does so smoothly, without stress on the components, and also ensures that the driver is always in the correct gear for his road speed in the event that he needs to pick up again. Many drivers also prefer to have the engine engaged with the driveline as this enhances both their feeling of control and their actual control of the vehicle. Heal and toe is very difficult and should be practised either on a private road or where you are sure there are no following drivers. I'd be interested to know who can do it; I can't; also a lot of cars do not have their pedals arranged very conducively; the old floor hinged 911 pedals were ideal as are the pedals in a manual BMW.
It has been suggested that a driver may choose to slow the car using only engine braking. This is dangerous as following traffic is given no indication that he is braking. Use of the brake pedal lights the brake lights, obviously; crashing down the gears does not.
There is absolutely nothing wrong with skipping gears on the way up or down the box. The important thing is to be in the correct gear for your road speed and intentions. By way of example, when joining a major road with fast moving traffic from a standstill, a driver may use maximum acceleration in first, second and third gears in order to reach the speed of the traffic as quickly and safely as possible. Having reached that speed, it is entirely appropriate to slot the car from third to fifth or sixth (if your vehicle is so equipped): he has got to the speed he wants to cruise at, so there is no need for intermediate gears. This can be a smooth and efficient way of driving.