You can make them with a lathe. It's slow, PITA work, but can be done, just not as profitably as many other things you can do with the same time and lathe.
You can increase production by buying a turret lathe, which is a manually operated repetitive operations lathe, but then you have to find a decent affordable one, and learn to set it up for use.
Or you can invest heavily into CNC lathe and tooling to do the same, more money,even more other more profitable things that can be accomplished. Starting to see the trend?
The big companies use progressive deep drawing to form blanks from slugs punched out of brass sheets or roll stock. Each die squeezes the blank out as they automatically progress through the whole series, depending on the size and the case shape. There are usually steps along the process that involve heating the whole blank or just parts of it, to anneal, as well as processes to clean off accumulated dirt and built up lube.
The machines are big, expensive, and require a machine shop full of competent machinist/toolmakers to keep them supplied with dies as they do wear out at a pretty good rate. The expense of operating them is one of the main reasons that certain calibers have fallen off the map, as they required blanks that were of a size unique to them, and it was not profitable to make them when the same machines could be making cases that could be formed into many different products.
Yer internet skills must be ... never mind.
Google Images search the term "Making Brass Cartridges" and you will see some of the results.
Yer not gonna do this at home unless you have a half million or so to spend, and some talented employees working for you. The machinery is called a progressive deep drawing machine or press. There are a LOT of more profitable things to do with one of them, again.
DIY with a lathe is about your only option, unless you can convert another case to fit.
Cheers
Trev