How do players qualify for the Presidents Cup?

To automatically make the American team you need to a US PGA Tour member and finish as one of the top 6 Americans in Fed Ex Cup points post the 2022 BMW Championship. If not, you can hope to be one of 6 Captains Picks after the BMW. There are 8 automatic qualifications for the International team based, fundamentally, on World Rankings. 4 Captains Picks will complete the team of 12.

More about how players qualify for the Presidents Cup

FedEx points for the USA team are 2019 through to 2022, not just the current season. 

Because you have to be a member of the USPGA Tour to make the USA team this immediately excludes all LIV players - pending any legal outcomes. It would seem most unlikely any Captains Picks will go to LIV players.

International team selections are not exactly based on OWG Rankings but use the core data and process to select players who earn points from the 2021 Open through to the 2022 BMW, with some tweaks to the actual calculations.

At the time of writing LIV results do not earn OWG Rankings so again, it's very unlikely we'll see any LIV players on the International team.