Probably using the same fair market value that pre-IPO startups calculate to assess your tax liability when you exercise options.

Lots of ways to value a company. Once you have the value of the entire company, the price per share just depends on the number of shares. Options are then calculated based on a formula using the price per share as one input.

You can value a company by comparing it to its peers (this is like company Y which has similar users, growth potential etc)

You can value a company by only caring about its assets and liabilities.

Private shares of a company can exist and be traded, another market based valuation just with fewer data points that are private and not publicly shared.

And plenty more ways. Finance is really all about answering this question, how much is something worth and then creating mechanisms to trade that value in different ways.

You generally use 409a valuations, which increase in regularity and accuracy as the company matures (ie. gets bigger and closer to an actual IPO).

As a former Uber employee, I assure you they do not become more accurate. It’s all based on funding rounds etc. The stock market is a different beast altogether.

Maybe off of current worth estimated after sale of shares to earlier investors? I'm not completely sure though.

When I worked at a pre IPO startup they always used the valuation of the last investment round.

Same way you do after an IPO. Based on the sale price of the stock.

409a valuation.