The only explanation we have on Vivre Card so far is from chapter 489, when Lola explained it to Nami. At that time, Lola was pretty vague, but that's the only thing we know so far. We are about to meet Vegapunk in a few days (a few years in real life probably), so we might know more when Smoker and Tashigi reach him.
How are they made?
Lola explained that there are indeed specialized shops that make those cards and that the process to make such cards is just to put the owner's fingernail in a mix and create a special sheet of paper with them, but she did not specify the mix that is needed or the way to transform the mix into the actual sheet of paper.
Are they only made in the New World?
The translation I have used in the below screenshot says that
Bibli Cards only work in the New World,
which we know to be false, since the Strawhats used Rayleigh's Vivre Card on the Grand Line. I have found a different translation that says that
Vivre Cards are only available in the New World.
So to me that sounds like only the New World has specialized shops to create such cards, but if you know the process to making them, you could make them anywhere.