Learn Spanish (Spain): Son dos euros y cincuenta céntimos.

In Spanish, when stating a price, the verb matches the number. Because two euros is plural, you use son (they are). If the price was exactly one euro, you would use the singular es to say es un euro.

Why do we use y (and) instead of con (with) for the cents?

In Spanish, you simply connect the main currency and the cents with y (and), exactly like saying two euros and fifty cents in English. Using con (with) for prices sounds unnatural here.

Is céntimos the standard Spanish word for cents everywhere?

No, céntimos is the word used in Spain specifically for euro cents. In most Latin American countries, the word for the cents of their local currencies, like pesos, is centavos.

Do I always have to say the full phrase, or can I just say two fifty?

Just like in English, if the currency is obvious, people often shorten it in everyday conversation. You can simply drop the currency names and say son dos cincuenta.