Why would the vice president take over the president's job? Who becomes president if the vice-president cannot serve as president?

Think of it as a giant chain. You have the President at the top, then followed by the vice president, and so on to the bottom of the chain. if the first link of the chain is broken, then you replace it with the chain link below it. So, the Vice president would replace the President, the Speaker of the House of Representatives would replace the Vice President, and so on.