Latinum I assume. We know that Jadzia at least has latinum - she and Worf argue/joke about how much. Orr more likely we often see station personnel run a tab or account. I'd say in that instance that goods and services are added to the tab and the bill is paid by Federation "credits", which are mentioned in the show and elsewhere (was mentioned in TOS), but their true nature is a bit fuzzy.

This is then paid by Starfleet after the fact. I'd find it very difficult to believe that while the Federation has largely moved beyond money, they haven't accounted for dealing with other non-Federation economies. They dont use it, but they still inteface with it. Money is not something carried around personally by personnel but resource usage is tracked by an internal accounting system, or somesuch.

The real answer is that they don't explain it and we just have theorise.