Hitchhiking usually implies that no money changes hands, no monetary transactions for the ride.
How to deal with requests for money beforehand
In Western Europe and the United States it's rare that people ask for money. It can happen though, especially in Germany, where Mitfahrgelegenheit is quite popular. As a rule guaka refuses these rides, though once he accepted a ride because it was later at night after having waited for a long time already and he didn't feel like waiting any longer.
In some countries payment for rides is quite normal, especially for locals. In Romania for example you probably want to ask if the ride is free (how to ask this in Romanian?). In Turkey it's rare, but it happens that drivers want money, just say "yok parra" in such a case.
What to do if a driver requests money unexpectedly
What to do if a driver offers money
Some hitchhikers (such as guaka) refuse any offers for money from the drivers. Sometimes drivers are insisting, but if you have enough money to go by and you think it's inappropriate to receive money, you could tell them you actually have plenty of work (and income), that you mainly hitchhike for fun, social contact, and ecological reasons.
Others will happily accept any money they can get.