It is the same as public markets, but just on a smaller scale. Instead of millions owning a % for $X, you have a few individuals/firms who agree % for $X. And you (the company) can exchange - tender offers, private sales, etc.
"Structuring" makes a huge difference. VCs will invest $10mm for 10% of a company, making it apparently "worth" $100mm. However, they will get guarantees such as a right to the first 30% of profit before any other investors get paid back. It's not straightforward to know precisely how deals like that that translate into the final value of the company, but it's a guarantee that it's less than $100 mm, and with harsh enough structuring the actual value of the company could be closer to $10 mm.
The same... with no public scrutiny, last trade price most likely reflecting a primary sale (i e. the market only contains buyers), and very few sample points overall. That's not the same confidence of price, even if the structure is analagous.
Public markets at least have some degree of liquidity. You can turn that paper into cash if you wanted to.