In a double-slit experiment, interference patterns are shown when light passes through the slits and illuminate the screen. So the question is, if one shoots a single photon, does the screen show interference pattern? Or does the screen show only one location that the single photon particle is at?
The answer is yes to both questions: yes, the screen does show one location for one particle and yes, the accumulated picture after repeating the experiment many, many times does show the interference pattern.
There is a set of beautiful pictures and a video of the double slit experiment in one-particle-per-time mode that can be found here (the experiment is with electron but conceptually there is no difference).
Let me try a slightly different way to answer this (well worn) question.
The photon doesn't have a location, or at least not a well defined location, until you interact with it and cause it to localise.
When the photon hits the photomultiplier, or photographic plate, or whatever you're using as the screen the interaction occurs at a point and that localises the photon. Until then it's somewhat meaningless to talk about the position of the photon. I don't mean the photon has a position but we don't know it, I mean the photon simply doesn't have a position. That's why it doesn't make sense to ask which slit the photon went through. because the photon's position is ill defined it occupies the whole experimental apparatus.
So a single photon does indeed passthrough both slits, but it then interacts with the screen at a point. The point of interaction with the screen is random, with the probability o the position being given by the square of the wavefunction. That's why over time the pattern created by many phtons gives you the interference pattern.
We don't know whether the light source shoots photons or not. We know that if we turn off power to the light source the interference pattern disappears, and that if we turn down the light intensity enough we eventually start seeing individual events, if we have the right sort of measurement apparatus. Again, if we turn off the power those individual events stop (except for the "dark rate" that is characteristic of the detector), so it's definitely the light source that is causing the individual events, but we don't know what happens in between.
It's possible to account for this simple kind of experiment using a semi-classical model in which there is an electromagnetic field between the source and the detector, and the detector current flips off and on. It's only when we consider more sophisticated experiments, in particular in which we engineer the light sources so that two or more individual events are closely synchronized in time, that we find that neither shoots photons nor there's an electromagnetic field works very well.
Consequently, we might or might not be able to satisfy the premise of "if one shoots a single photon, ...", making it not possible to answer the question with certainty with our current understanding. Nonetheless, I up-voted Slaviks Answer, because that's what is usually said.
After 2006, no philosophic duality exist, only bad pictures
As @Slaviks says, "the answer is yes to both questions", but I like the modern and experimental (!) Y. Couder interpretation. See by your self (!),
The quantum particle HAVE a location (against @Rennie says), there are no "philosofic duality", there are only a limitation in choose a good pictoric model when you is constrained by "wave or particle" picture options: Couder demonstrates that a good picture, of an "intermediary wave/particle object" model, exists!
Imagine a "localizable object" that haven't a well-defined boundary, but have a well-defined distance-limit (lambda) to interact with obstacles (other objects).
There are an article online about the experiment.