How to pay for something?
Having cash at hand works almost everywhere, but just almost. When paying to any company or institution which doesn't have its own cash register service, you have to pay via account, which means going to your bank, or nearest post office with a pre-filled (or not) payment order (aka "virman", "uplatnica"). It's simpler than it used to be, specially now that the post offices (and very small ones, with a single-person stall) have computers and document printers, so you only tell the girl there what to fill in and she'll type it. This still means you can't pay on the spot where you're buying - you have to take the uplatnica elsewhere, pay, get two copies of the stamped uplatnica (one for you, one for the seller) as the proof of payment, then bring one and finally get the goods.
The reason for this is probably the suspicion that any entity handling cash would be prone to swindling some amount behind the back of the state (in previous times) or tax authorities (nowadays), so the regulations are heavy. Many just won't bother with it and are satisfied to have the money land on their account, without the hassle of handling the cash and the accompanying paperwork (and the VAT reporting hardware and service, which is a considerable cost to small businesses).
Checks should still work, but I haven't seen anyone using them (for now). It used to be a form of loan (this way or other), where you'd write a check in advance, sometimes without a date, sometimes with future dates, and the seller would cash these checks later. The benefit was mutual - the seller had a secured payment (albeit in the future), and you didn't have to have the cash immediately. I had such an arrangement for milk and cheese at the nearby kiosk - I'd leave a dateless check with some round amount on it, kept buying until the amount was spent, then the clerk would ask me to put a date on it and she'd cash the check in a few days.
One thing that I haven't heard of as feasible is mailing a check. Nobody sends you a bill with an envelope in the envelope. It's just not done, for reasons I never understood.
Plastic works... mostly. The readers are mostly new and they read the chip first; if no chip, they read the magnetic strip. The ATMs (called "bankomat" - a more appropriate name, IMO) are concentrated downtown and at bigger shops (with appropriate security). Cards also work in larger supermarkets or stores, although you can't really guess who may have them and who not. Even if you have a debit card and type the PIN, you still have to sign, sometimes twice, which sort of defeats the purpose - plastic was supposed to be faster.