How do partners/employees make money with it?

Sell their stock for money, or stocks owned may pay dividends, or both.

When you hold stock, don't you need to sell it/liquidate it in order to make money?

Yes. But only a small percentage of the employees are retiring and selling their stock at any given time. There are usually limits on how and when employee stock awards can be sold before retirement.

And how do you hire somebody?

The usual way. After hiring, hires receive stock as a part of their compensation.

Do you sell your shares to the person at no cost or something?

It's just part of their compensation. Longer tenure employees end up with more stock earned over time, and may also receive more stock per pay period to reward loyalty.

Implied question: If employees can sell stock won't the company eventually be publicly traded?

There lots of ways the rules for holding the stock can be structured to prevent that, while still having real monetary value to retirees.

It's a bit much for a post here, though. And it varies by country, I think.