How do you activate the Grandmapocalypse?

You can trigger the Grandmapocalypse by purchasing the "One Mind" upgrade from the Research Facility.

If you don't have a Research facility yet you can unlock it by having the "elder achievement" (have at least 7 different grandmas).

Once you have the research facility you will have to keep buying the upgrades that it unlocks until the "one mind" upgrade becomes available, which should be the 6th one. Each upgrade takes about 30 minutes to research and become available. Note that you need to purchase an upgrade before the next upgrade begins researching.

You need to have 15 farms, mines, factories, banks, temples, wizard towers, and shipments each, first, and buy the corresponding grandma-related upgrade, such as “Miner grandmas” or “Cosmic grandmas” and then you have access to the Bingo Center/Research Facility upgrade, taking you through 4 other research/facility upgrades and then the “One Mind” upgrade, and that starts the grandmapocalypse․ The catch is that Bingo Center/Research Facility upgrade is 1 quadrillion cookies, and the cost doubles for each further upgrade you go into, capping at 32 quadrillion for One Mind. (It keeps growing for the 4 that come after, though, including Communal Brainsweep and Elder Pact). Find out more at https://cookieclicker.fandom.com/wiki/Cookie_Clicker_Wiki