It is true that there is a family in Johto which can fashion them out of apricorns, that Silph Corporation has made outstanding strides in making wholly synthetic ones, and that across the sea a different, mushroom-like pokemon is used. Nonetheless, throughout human history, the overwhelming majority of Pokeballs have been made out of the corpses of Voltorb.
It is a surprisingly simple conversion, requiring only the removal of most of the pokemon's internal organs, a few alterations in wiring, and the placement of a button to open and close the pokemon's body. Artisans in the old days could go through a hundred a day; modern assembly lines do so even faster.
Initially, the secret of the Pokeball (along with the pokemon themselves) was a closely guarded secret by the rulers of Lavender Town, which governed the Power Plant. Although the reasons why Voltorb corpses treated in this manner can shrink, capture, and domesticate pokemon are still not understood by science, the secret itself could not be guarded for long. Trainers who had previously resorted to elaborate pokemon-taming techniques soon paid enormous sums for Voltorb, which were shipped around the world despite their tendency to explode. Lavender Town, for its part, gained in wealth what it had lost in power.
Today, synthetic pokeballs (often blue or gold instead of red, depending on their effectiveness) appear to be the future of pokemon training, and are increasingly used for trainers who compete in the Pokemon League. The low cost of a Voltorb-made one, however, continues to make it the overwhelming favorite among the average trainer. Large farms of Voltorb can still be found in secluded areas, where they are killed once they reach maturity so they can be turned into Pokeballs.