For example, google.com. When this domain is approaching expiry, does Google pay the usual price for a .com renewal? Or is there a premium added for it being such a high value domain? If so, who decides this price?
An organization called ICANN (The Internet Corporation for Assigned Names and Numbers) contracts with registries to manage the registration of top level domains (TLDs). In the case of .com, Verisign is the company who manages that TLD. Verisign then works with registrars to resell .com domain names. ICANN places limits on how much Verisign and registrars can charge for the registration of a domain.
So, for Google, who is a registrar, the price to register their domain is the same as any .com domain. The fact that it is "valuable" plays no part in its registration price.
So why do some domains sell for millions of dollars? These domains are resold and are not part of the ICANN controlled registration process. In fact, it is just a domain transfer with the same registration fees charged as any domain transfer with the millions of dollars occurring as a separate business transaction.