Dynamaxing increases a Pokémon's size drastically, as well as changing the moves of the Pokémon and increasing their HP in battle (except for Shedinja), but can only be used once during a battle, and ends after three turns or if the user is switched out. In addition, it can only be performed in areas known to have Power Spots, such as Galar's Gym Stadiums, Battle Court, and Battle Tower. When Dynamaxed, all of the Pokémon's moves will turn into Max Moves that correspond to those moves' types and categories. Like with Mega Evolution, Dynamax is activated at the start of the turn before all other moves are executed. If a Dynamax Pokémon runs out of PP of one move, it still can be selected but fails, if is unable to use any moves (e.g. running out of PP), it will use Struggle.
Similar to Z-Moves, the type, damage category and base power of Max Moves that a Dynamax Pokémon knows depend on the moves it knew before Dynamaxing. The exception to this are status moves, which instead all become the Normal-type Max Guard. If the base move's type is changed either by a move's effect or an Ability (e.g. Pixilate, Electrify, or Weather Ball), then the Max Move will also be converted to that of the new type with the same power; however, the move selection screen will still display the Max Move of the original type. For instance, if a Fighting-type Silvally knows Multi-Attack, the Max Move will still display as Max Strike, but when executed it becomes Max Knuckle.
Damaging Max Moves deal 25% of their total damage against targets that use protection moves (such as Protect and Spiky Shield), and secondary effects are still applied. Only the Max Move Max Guard fully protects against Max Moves. Secondary effects of Max Moves may also affect targets and their allies behind a Substitute. Max Moves also never miss, unless the target is semi-invulnerable.
For Gigantamax Pokémon, damaging moves of a certain type become its exclusive G-Max Move instead of the normal corresponding Max Move; the type of moves affected depends on the Gigantamax Pokémon's species. Eternamax Eternatus can also use Max Moves, but this form cannot be obtained by the player.
These are the basics. Anything else would make this answer way too long, so if anything else needs explaining, check my sources. If you have any other questions about Dynamaxing, I'll edit the answers in.
Hope I helped!