How to declare a function that throws an error in Typescript

There is no such feature in TypeScript. It's possible to specify error type only if a function returns an error, not throws it (this rarely happens and is prone to be antipattern).

The only relevant type is never. It is applicable only if a function definitely throws an error, it cannot be more specific than that. It's a type as any other, it won't cause type error as long as it doesn't cause type problems:

function Test(): never => {
  throw new Error();
}

Test(); // won't cause type error
let test: boolean = Test(); // will cause type error

When there is a possibility for a function to return a value, never is absorbed by return type.

It's possible to specify it in function signature, but for reference only:

function Test(test: boolean): boolean | never {
  if (test === true)
    return false;

  throw new Error();
}

It can give a hint to a developer that unhandled error is possible (in case when this is unclear from function body), but this doesn't affect type checks and cannot force try..catch; the type of this function is considered (test: boolean) => boolean by typing system.

You can mark the function with @throws jsdoc at least. Even though it does not provide static analysis errors in typescript compiler, some good IDE or linter may still report a warning if you try to disregard the function that throws...

/** 
 * @throws {Error}
 */
function someFunc() {
    if (Math.random() < 0.5) throw Error();
}
someFunc();