There is some debate as to which cities constitute the Golden Circle. Soviet officials were not inclined to tolerate such ambiguity, and therefore created an official list: Ivanovo, Kostroma, Pereslavl Zalessky, Rostov Veliky, Sergiev Posad, Suzdal, Vladimir, and Yaroslavl.
Since the cities have similar architecture, it is seldom worth visiting them all. Most visitors only make four–six stops. The most fascinating is Suzdal (near Vladimir) and so these two are worth a combined trip. Sergiev Posad is also worthwhile (and easily accessible from Moscow). For those with more time, Yaroslavl may also be worth a visit (perhaps combined with a trip to Sergiev Posad). None of this is to say that any of the destinations included below are not worth seeing—quite the contrary! But it is worth picking and choosing the ones that interest you most.
The vast majority of international visitors arrive via Moscow and its big international airports. But you can get to the individual destinations on the circuit with relative ease from any nearby part of Russia—Russia's intercity rail network is extensive and fairly efficient, supplanted by a more confusing and less efficient bus/marshrutka network. For those interested in hitting the path less (far less) beaten, the other possible international point of entry is the airport in Nizhny Novgorod to the east. Another possibility is to book from Moscow a private guided tour to one of the destinations of the Golden Ring you are most interested in or take the tour along a number of cities of the Golden Ring.