Learn French: Ça coûte environ une cinquantaine d'euros.

Yes, it is literally "about an about-fifty"! However, this double approximation is extremely common in everyday spoken French. French speakers often combine environ (about) or à peu près (roughly) with an -aine word to sound extra casual or to emphasize that it is just an estimate.

How exactly do we form the word cinquantaine?

You take the number cinquante (fifty), drop the final e, and add the suffix -aine. Words ending in this suffix are feminine, which is why we use une.

Why is it d'euros instead of des euros here?

Because une cinquantaine acts as a noun of quantity, just like un litre or un groupe. In French, nouns expressing a quantity are followed by de (or d' before a vowel), rather than the plural article des. It translates literally to "a fifty of euros".

Could I just say Ça coûte environ cinquante euros without using the suffix?

Absolutely. Environ cinquante euros and une cinquantaine d'euros mean the exact same thing. Using the -aine suffix simply gives you another way to express estimates and makes your French sound very natural.