In short, to download Phantasy Star Online 2, you must have a Steam account and then download the game via the Steam store page. If you have the base game already installed, you won’t need to download it as both games will use the same launcher.
That being said, you can find the game over at its official Steam store page, and to start a download for it, you need only hit play now. After this, the game will be added to your account, and you can then start a download for it by selecting a place on your computer for it to install to.
Related: All weapons in Phantasy Star Online 2: New Genesis
Once you have your install folder selected, wait for the game to download, and when it finishes downloading, launch the game.
At this point, you can then load into Phantasy Star Online New Genesis by selecting the option to do so from the in-game menu. You can also load into the base game, Phantasy Star Online 2 by selecting the option to do so instead of New Genesis.
You can even transfer your character from Phantasy Star Online into New Genesis via the character transfer option when you create your character.
For more on Phantasy Star Online 2: New Genesis, check out and What is the release date for Phantasy Star Online 2: New Genesis?