What happens to options when a company goes private. For example, if I have a call option on Tesla right now and it goes private at 420/share, what will happen to my options?
You get force-liquidated with the go public price as reference.
I.e. if you have an option to buy at 400USD, you get 20USD (all per share).
When a stock is converted into a right to receive a fixed amount of cash, its options will be adjusted to require the delivery upon exercise of a fixed amount of cash ($420 in your example).
On the date of the buy out, option trading will end and all out-of-the-money options will be worthless and all that are in-the-money trade at their intrinsic value. For a call, the intrinsic value will be the stock's price less the strike price and for a put it will be the strike price less the stock's price.