I can't speak to OpenAI's specific setup, but a lot of startups will use a third party service like Carta to manage their cap table. So there's a website, you have an account, you can log in and it tells you that you have a grant of X shares that vests over Y months. You have to sign a form to accept the grant. There might be some option to do an 83b election if you have stock options rather than RSUs. But that's about it.

In my experience owning private stock, you basically own part of a pool. (Hopefully the exact same classes of shares as the board has or else it's a scam.) The board controls the pool, and whenever they do dividends or transfer ownership, each person's share is affected proportionally. You can petition the board to buy back your shares or transfer them to another shareholder but that's probably unusual for a rank-and-file employee.

The shares are valued by an accounting firm auditor of some type. This determines the basis value if you're paying taxes up-front. After that the tax situation should be the same as getting publicly traded options/shares, there's some choices in how you want to handle the taxes but generally you file a special tax form at the year of grant.

Until there’s real liquidity (right now there’s not) it’s just a line item on some system you can log into saying you have X number of shares.

For all practical purposes it’s worth nothing until there is a liquid market. Given current financials, and preferred cap table terms for those investing cash, shares the average employee has likely aren’t worth much or maybe even anything at the moment.

It's just an entry on some computer. Maybe you can sell it on a secondary market, maybe you can't. You have to wait for an exit event - being acquired by someone else, or an IPO.

You got the right idea there. They wouldn't actually show up in your Fidelity account but there would be a different website where you can log in and see your shares. You wouldn't be able to sell them or transfer them anywhere unless the company arranges a sale and invites you to participate in it.

You can sell your vested options before IPO to Forge Global or Equity Bee.