Learn Russian: Это золотое кольцо.

When saying "This is a [noun]", you always use the fixed word Это, regardless of the noun's gender. For example, "This is a car" is Это машина. It just happens to look like it matches the neuter noun кольцо in this specific sentence.

Why does the adjective золотое end in -ое?

Adjectives must match the noun they describe in gender, number, and case. Since кольцо (ring) is a neuter noun in the nominative case, the adjective takes the standard neuter singular ending -ое.

Since our current lesson is about the dative plural, what would "to the gold rings" look like?

It would be золотым кольцам. In the dative plural, hard-stem adjectives take the -ым ending (becoming золотым), and neuter nouns usually take the -ам ending (becoming кольцам).

In English, we just use the noun "gold" to describe the ring. Why do we need the longer word золотое in Russian?

In Russian, you usually cannot put two nouns next to each other like "gold ring" (золото кольцо is incorrect). You must turn the material into an adjective. From the noun золото (gold), we get the adjective золотой (golden / made of gold), which becomes золотое here to match the neuter noun.