Well, after singing for a while with a teacher I kinda understood how to produce a good steady voice. However, it's a bit difficult to explain in text.

But okay, this at least was the revelation for me: try to blow air like blowing out a candle. Meaning a directed, focused blowing that comes with a good strength. This is basically how you want your breathing to be when singing. A steady air flow, without muscular tensions. Then, you just slowly add voice to that air flow. With a humming voice first, trying to utilize as much of your vocal cords as possible. Then you can try singing louder, and seeing if you can keep the same steadiness. What you are trying to get the hang of, is a certain "bite" where your voice resonates with a good clarity and has strength to it, without really trying too hard. (Go watch John Denver singing to know what I mean)

An issue I, and probably many others, face is an inefficient breathing that generates friction in your vocal cords, causing your voice to quickly fall apart becoming weak and crackly.

So avoid "pushing" your voice as much as necessary. It will just cause bad muscle memory, like doing deadlifts with a bad technique. You have to build up the nervous system and the muscle memory slowly, never extending it too far. It might feel annoying singing with "half-volume", when all you want to do is to sing along with your favourite singer with full power. Yet once you build up the technique the whole thing becomes significantly easier. Hard to explain, but you shouldn't be feeling like you have to expend a lot of effort to get a strong voice.

Well, I hope that's something. I would be curious to know if it helped.

Or even not alone - is it possible to get better at singing, or is it mostly just natural? I can kind of "hold a note", but only about 8 of them! Can you meaningfully extend your range, or is your range your range?

Rock Band, SingStar etc will tell you when your pitch is off. It won't help you with anything beyond that, but it's a start.

As someone who's been learning to sing mostly on my own (though I've taken a few local workshops that have helped a lot), here are the things I've found most helpful:

* commit to the notes you're singing: singing tentatively makes it harder to evaluate yourself

* sing along with a recording and emulate the singer--every ornament, every nuance in timing--you can find your own voice (so to speak) once you know what you're doing

* repeat a song or even chorus or line over and over, especially singing along with a recording

* record yourself: everyone hates doing this, but again, it's much easier to evaluate what you're doing

* if you're having trouble with a specific line, find the notes on an instrument and sing along (though make sure you're not just locked in to fixed pitches--a lot of the beauty of great singing is exploiting the marvelous glissando capabilities of the human voice)

* drink water and don't hurt yourself

Here:

    sudo apt install audacity

('audacity' is a sound recording program.) Then try to sing along a YouTube song, listening to the song in your headphones, whilst singing into a mic — recording your voice only.

Then play back your voice, from the recording, and find out what you'd like to change about your voice, and what you can get better at. It's harder to sing, than what I thought!

And, juts like running or table tennis or whatever, everyone is going to be not-good at it, in the beginning, I think.

Unfortunately, singing is pretty hard to learn alone. Correct technique is somewhat unintuitive and it's hard to actually see what other singers are doing (internally, with their muscles, throat, larynx) and compare it to what you're doing.

When taking lessons is not an option, I've seen this course get recommended at /r/singing a lot: https://singingsuccess.com/

Don't have first hand experience with it, though.

You really need a voice coach, because you really can't hear yourself sing. Crazy but little known fact-- even professional soloists hire voice coaches. A former coach of mine works over Skype, though I never tried that.

I used Rock Band for this for a while.