There’s no central place where currencies are traded.

Instead, large banks advertise an interbank rate that they will trade at - they do that by sending information to all the other banks through a wide range of e-trading platforms - including Bloomberg and platforms run by other banks like State Street, Deutsche etc.

There is a huge volume of transactions happening every minute - so prices tend to harmonise very quickly. Banks set their prices based on their internal supply and demand. If a bank is offering a good price, other banks will deal with them until they have exhausted that bank’s offer. If a bank offers a bad price, no-one will trade with them until they raise their offer.

Information services like Bloomberg, MorningStar and many other capture that information and make it publicly available - normally on a slight delay to the general public.

Many governments also require banks to report to them on fx rates in parallel to the above.