Here is an easier, simple way to go into "slow smooth breathing" as a form of meditation.
You don't have to control the breathing itself at all. In fact, that's guaranteed to interfere with it and make it not smooth. I've tried that before, controlling the breathing muscles etc and it takes much longer to work up to a slower smoother breath.
Instead, think of a balloon. The balloon is inflated. You take the opening of the balloon and you open it up just a little bit, just enough to let some air seep out. You then HOLD that opening at the same amount of openness, without moving it. What happens? The balloon deflates VERY smoothly all by itself.
The smoothness and rate of airflow is PRECISELY controlled only by how big the opening is. It's got nothing to do with you squeezing the balloon, trying to make the balloon collapse at a certain rate, etc. So the trick here is, do not try to control the breathing ITSELF, whatsoever. All you need to do is regulate the SIZE OF THE OPENING and keep it steady, which is very easy.
1. Close your mouth, breathe through your nose.
2. Hold your breath for a moment then let it go. Try that a few times. There is a sensation of some muscles in the throat closing off the airway. There is also (i think) the nasopharynx which is kind of in the back of the nose, behind the soft palette. This action of holding breath closes the nasopharynx so that no air can go in or out of the nose. So it feels like the back of the nose is closing and opening.
3. You have the ability to decide "how open" that thing is. This is a physical action above the throat and nothing to do with the lungs or diaphragm. Close it off again but not all the way. Just tighten it up a bit and try breathing out while it's "almost closed". You'll notice even if you try to push the breath harder to come out faster it won't. It can only come out at a rate determined by the size of the air opening. So you can operate this kind of like an air valve.
4. So this is all you need to do. Just "mostly close" that "valve" and hold it in that position. Relax. Let your body do its own normal breathing without you trying to mess with the breathing at all. Don't push the breath or pull it or try to make it slow or anything. You don't need to. Just because the opening is narrower, your breath will be long and slow and smooth.
5. Relaxing your body, just let it breathe, while you hold that opening in a partly closed position. Notice how the body just naturally "inflates" long and slow, like a balloon that inflates by itself. Then when it's done, as you keep holding the valve partly open, it starts to deflate all by itself, like a big bag of wind which just gradually empties by itself under its own air pressure (actually the normal diaphragm action).
So I do that a while. It's MUCH easier to just hold that position of restricting the outlet, than it is to try to manipulate the breathing muscles. I just hold it a while and let the body breathe slowly by itself. It's effortless, especially when you relax. "How slow" you breathe is entirely determined by how much you close off the airway, and nothing else. You can go immediately into a long slow breath without having to work up to it, and it takes hardly any effort. After a while you should feel calmer and your mind is "smoother".