Joshua is right. You will find many comments on the web that upturned stigmas indicate successful pollination. It's really a hope, not an absolute reality. But, while an upturned stigma may or may not indicate anything, I think you can be sure that if the stigma does not turn up, there was no successful pollination.
How long it takes for actual fertilization of the ovary to occur is highly dependent on temperature, the species background and length of the pistil. I am guessing it would take anywhere from a day to a week.
