Unless the pizzeria in question is telling you that they use a natural culture, it's almost a certainty that they are using baker's yeast (ADY, IDY, or CY), so it is very likely the culture you end up with will be one you could create simply with yeast from the grocery store.
There is no "right way" to create a culture from a dough ball. You are just using the dough to inoculate a flour-water mixture.
I would let the dough ball rise up until it starts to fall (keep it covered so it doesn't dry out - mist it if you need to). That should give you peak yeast activity. I would then mix equal parts by weight of flour and water - maybe 150g of each, cut up 50g or so of the dough into little pieces and mix it in until everything is relatively smooth. Feed it equal parts of flour and water every couple days.