Let's begin at the beginning. You arrive in Croatia by plane, train, boat, bus, ferry or car. You have to pay a taxi driver or bus driver or you need a cup of coffee. In a pinch, you can pay with euros, US dollars or pounds sterling (bills only; no coins) bearing in mind that the exchange rate will be unfavourable and your change will be in euros.
Still, you can get by until you can reach an exchange office (Mjenjacnica) or an ATM.
Airports, bus stations, train stations and ferry ports that receive international arrivals (Zagreb, Split, Zadar, Dubrovnik, Rijeka) will have a convenient exchange office to change money but they are not 24/7 operations! For a late-night arrival, look for an ATM. Exchange offices are, of course, money-making operations so you will pay a commission of about 3%.
Another option for quick cash is to head for a big hotel. They will be only too happy to hand over local currency but, as the exchange rate is terrible, this is a last resort only.
Banks and post offices will also change money at about the same rate as exchange offices but their opening hours are shorter.