The factors involved in natural selection are not necessarily fixed at 4; in many ways, it's a matter of perspective and context, ie. what is taken for granted, and what is assumed, about the population and ecosystem being inspected. We might interpret this question to say "what four factors most directly influence natural selection occurring as opposed to another form of selection, such as sexual or artificial."
The four primary factors are;
- Variation exists within a species. This is largely the result of mutations and meiotic gene shuffling. Variation allows for the possibility of certain variations being more fit than others.
- Species overproduce. This means that they have more offspring than their environment can support. If they had less offspring than the environment could support, then a surplus of resources or lack of competition would not place the same selective pressure.
- Competition exists. This can be intraspecific or interspecific competition, but in most ecosystems it is likely a little of both. Competition causes certain variations to be more capable of succeeding in the competition than others; a lack of competition would make the variations largely irrelevant.
- Inheritance. If the offspring of individuals inherit their parent's traits, this ensures that certain aspects of variation will endure; fit individuals will produce fit offspring, and unfit individuals will not produce magical, super-fit babies for no apparent reason.
We must be careful to frame some of these factors in the proper persepective; for example, competition among plants does not mean that two plants are eyeing the same grassy hilltop and shooting each other dirty looks. In fact, most of the time, there is no "intention" in the human sense behind most of these factors, but rather they are simply the way the world is described from the perspective of long-term ecological change.
In addition to the above answers, there must also be an evolutionary need for certain traits to be inherited. If the ecosystem fully suports the population, or if there is no reason for "the fittest" to survive because all individuals are supported by the environment, all genes will (in theory) be passed on equally. In short: if there are no genes that give an evolutionary edge to the species there can be no natural selection.