Gigantamaxing Pokémon isn't a particularly complicated or difficult process. The trick is in finding Pokémon capable of the Gigantamax transformation. Here's help with both.
How to Gigantamax Your Pokémon, Explained
Gigantamaxing is an even more extreme version of the Dynamax transformation mechanic introduced in Sword and Shield. Where Dynamaxing a Pokémon makes them larger, Gigantamaxing takes that growth to the next level, making Pokémon truly enormous.
Both mechanics are activated in the same way: by feeding one of your Pokémon a Dynamax Candy. This transforms them into a Dynamax form of themselves for three turns.
Dynamaxing, and by extension Gigantamaxing, can only be done in certain environments: during Link Battles with other players, in Max Raid Battles in the Wild Area and in Stadium Battles.
Only specific Pokémon in Sword and Shield can Gigantamax instead of Dynamaxing, and not all of the Pokémon of those species can Gigantamax. You can check whether a Pokémon can Gigantamax by looking for a red X symbol between its name and the Poké Ball in which it lives.
Here are all the Pokémon species that have the potential to be born with the ability to Gigantamax.