The short answer to this question is simple: experience. The longer answer is also simple to understand but much more difficult for the dealer to put into practice: knowledge and quick thinking. Casino roulette requires a ton of quick thinking by the dealer and it is likely that they will eventually make a mistake, either by paying you more or less, so you also need to be aware of your winnings when playing in a casino.
Regardless, calculating winnings is not as difficult as it seems at first glance or from an outsider's point of view. Every box in which you can bet in roulette has a value assigned to it depending on the amount of money that you bet, so it becomes easy to calculate if you're half-decent at math. Most dealers are good at math and calculating, as that is a requirement for the job.
If you place a bet on a single number, the dealer will be able to quickly tell how much you can win by multiplying the value of your bet by the payout of the number at which your bet lands. The same goes for multiple number bets: they all have different values and the dealer can quickly tell how much money you've won because they've memorized the values and winnings of each bet. You can also play at digital casinos and save yourself the trouble of having to wait for the dealer to pay you. Use one of the following to play in reliable no deposit roulette casinos: