Follow the stops in order, from Postwick through the eight Gyms to the post-game and the two DLC areas. In the Wild Area you can only catch Pokémon up to a level set by your badges, so each Pokémon is listed at the first badge that lets you catch it. Tap a row to check it off. Evolves into shows later stages and how they evolve.
Shiny Charm: catch every Pokémon in the Galar Pokédex, then talk to the game director at Hotel Ionia in Circhester. You'll need trades for the other version's exclusives.
Alolan Diglett hunt
The Isle of Armor hides 150 Alolan Diglett. Look for their three hairs poking out of the ground and press A to find one. Report back to the man you meet with the first one when you arrive on the island, and he gives you rewards as your count goes up. Diglett are tracked by area.
Gigantamax Pokémon
Most Gigantamax Pokémon are caught in Max Raid Battles at the dens listed; a few are gifts or events. In The Isle of Armor, Max Soup made from Max Mushrooms can give a Pokémon you already have its Gigantamax Factor. Each one is a single check-off here, separate from the Pokédex.