Helium is produced naturally by radioactive decay underground. There is no way to artificially produce it in useful quantities.

But we can capture more of it from natural gas wells. Today much helium is just vented off and wasted at wellheads. As the price rises it makes sense to invest in cryogenic helium capture equipment for more wells.

Helium exists in great quantities in the 4 big planets, which unlike Earth have strong enough gravity to retain it.

Others have mentioned that some helium exists on the Moon, where it comes from the solar wind. The use of the helium 3 from there has been suggested for nuclear fusion, if the fusion of helium 3 became possible (it is much more difficult than the fusion of tritium with deuterium, which is the main approach attempted for now).

However, for fusion relatively small amounts could still be useful. For other uses the amount of lunar helium might not be enough, even when ignoring how expensive it would be to transport it from there.

It can form during radioactive decay of uranium and thorium.

Terrestial helium isn't produced by nuclear fusion. It's produced by nuclear decay. As you may know, you get alpha, beta and gamma radiation from decay. Gamma rays are just energetic photos. You typically need thick lead and/or concrete to shield you from them. Beta radiation is high energy electrons. A thin sheet of steel will shield you from those.

And lastly we have alpha radiation, which is just a Helium nucleus. A sheet of paper will generally block alpha radiation.

Some materials are really strong alpha emitters. A good example is Polonium-210 where almost all of its energy from decay is in the form of alpha radiation. This is why Po-210 is so lethal when ingested, which has been used for that purpose [1].

But this means if you produce a lump of Polonium-210, it's basically radiating Helium. The source of almost all of the Earth's Helium is from uranium and thorium decay.

[1]: https://en.wikipedia.org/wiki/Poisoning_of_Alexander_Litvine...

It's also formed similarly to oil over millions of years underground if I understand correctly so can be a byproduct of natural gas mining.

The reason helium can't be produced chemically (like hydrogen can be produced e.g. from water) is that there are no natural chemical compounds which contain helium. That's because it doesn't form those compounds in the first place, since it's a noble gas.

If you have something that emits a lot of alpha particles as it decays, you could surround it with a source of electrons, I suppose. The details would have to be left as an exercise, and I doubt you'd get enough helium to be very useful unless you were dealing with large amounts of ridiculously-radioactive substances.

Same with fusion. Due to the implications of E=mc^2, fusion yields a lot of energy and a uselessly-small amount of matter. There don't seem to be many good ways to get a lot of helium besides either waiting millions of years for it to show up naturally, or carefully recycling what we already have.

Atmospheric extraction on Earth would require massive amounts of energy and infrastructure.

Gas giant atmosphere extraction sounds very far future