'Golden' is a rather antiquated term, mainly used in fixed phrases, for example, golden hair, golden corn, golden wedding, golden opportunity, golden handshake. Many of these are idioms from an earlier era. Nowadays, we tend to use 'gold' for both things that are literally made of gold, such as 'gold ring', and also for things that are gold in colour but not made of gold. For example, we say 'gold ring' if the ring is actually made of this metal. The noun phrase 'gold ring' is made up of two nouns - the material (gold) and the object (ring). Nowadays, 'gold' is also used as an adjective meaning 'gold in colour'. For example, gold medal, gold paint, gold star, gold shoes. None of these things are actually made of gold ( the last Olympic gold medals that were actually made of gold were awarded over a hundred years ago), but we use the adjective gold to describe a yellowish metallic colour. If in doubt, use 'gold', unless you are using a known set phrase or old-fashioned idiom, such as one of the above.

The general rule is that if it is made of gold, then "gold", and when it only looks like it is made of gold, then "golden". Of course there are exceptions like "goldfish", they are obviously not made of gold.