Comparables, revenue multiples, discounted cash flow. There are multiple methods, none of them are perfect, but you can at least narrow it down.

The IRS isn't stupid. You can't do your own valuation - well you can, but they'll reject it.

Generally you'd hire at outside firm to do a valuation. If the IRS doesn't believe it, they'll come up with their own number and make you pay the taxes they think you owe.

Thiel basically made a bet - early investor when the company made $0, hence the value of the shares was effectively zero. His investment was in the thousands of dollars. He just got lucky that it had a huge pay out.