It seems that Pokémon GO surreptitiously provided Japanese media, including Famitsu, with some fresh details on the impending Max Battles mechanism a few days ago. We now know the following!

Step One: Find A Power Spot

You must gather 250 Max Particles in order to gain access to Power Spots.

Power Spots will appear in the game if you walk 2 km at the beginning of the new season. Unlike PokéStops and gyms, these will be treated as new locations rather than erasing the ones that already exist. The Power Spots are prominently displayed on the map and are indicated by the pink color.

Step Two: Join Max Battles

Challenge yourself and up to four other individuals.
One Dynamax Pokémon is all that is needed to participate; however, each participant may only have three Dynamax Pokémon on their squad.
This is a Max Battle that is only open to Dynamax Pokémon. It appears that finishing the course will allow you to obtain your first Dynamax Pokémon. Existing Pokemon are not eligible.
Apart from using power spots, strolling is another way to obtain the Max Particles needed to take part in the Max Battle. This option accounts for situations in which there are no power spots in the vicinity.

Step Three: Start the Max Battle

Max Meter → You can Dynamax your Pokémon when it reaches its maximum. Target visualization → When a Pokemon has three lines over its head, the Max Battle Boss is aiming for it.
This can be avoided by swiping to Dynamax. To do this, swipe towards an attack or the occasionally appearing Max Charge (purple button) to fill the Max Meter at the top of the screen to the maximum.
You will also need to teach each Pokemon its own Max Moves, which are useful for Dynamaxing.

Max Meter → You can Dynamax your Pokémon when it reaches its maximum. Target visualization → When a Pokemon has three lines over its head, the Max Battle Boss is aiming for it.
This can be avoided by swiping to Dynamax. To do this, swipe towards an attack or the occasionally appearing Max Charge (purple button) to fill the Max Meter at the top of the screen to the maximum.
You will also need to teach each Pokemon its own Max Moves, which are useful for Dynamaxing.

Each Dynamax Battle has a limited amount of turns to complete, which means more strategy needs to be implemented in order to defeat it.

Step 4: After Max Battle is All Over

You have the opportunity to capture the Dynamax Pokémon.
When a Pokémon is placed in a power location, it can aid trainers and other Pokémon in combat. Depending on how useful it was, you will be rewarded when it returns.
Boosting Pokémon Dynamax → You’ll need the right candies and Max Particles to strengthen a Max Move. Incidentally, you can increase its XP by reinforcing it.
During the GO Big event, you can find the evolved forms of Bulbasaur, Charmander, Squirtle, Skwovet, and Wooloo among the Dynamax Pokémon.