Typically, a PhD is not a job and thus a candidate does not have to have wage. Thus, it is not anyone's responsibility to provide any costs.
Professors, in different grades (but capable to be supervisors to PhDs), accept PhD candidates and conduct with them (as supervisors) novel research in various scientific disciplines. From this research, the candidate proves that he/she is able to hold the title of PhD and this whole process leads to the PhD tite (if the candidate succeeds).
Funding is side effect/project/what_ever. There are various opportunities for the state, country, companies to actually buy/fund novel research results and by this process there is a useful feedback from the scientific domain to the professional one which, in many cases, drives the production of new products and services.
So, if a Professor has a vacant position for a candidate and if the field of the research is close related or exactly at the field of a fund opportunity and if the Professor cares to apply for funding and if the application is approved then money can come for this research.
If the money finally come, then there is a usual division of labor with an appropriate "wage". These may (and is most likely that they do) vary between countries, universities, continents.
Thus, if someone needs to conduct experiments which need some money to spent then either the institution provide them, or he/she provide them, or the Professor has already a funding going on and cares to actually "hire" a PhD candidate to conduct the novel research based on the experiments.