Parapsychology uses methods commonly employed in other scientific disciplines. Laboratory studies use research methods from psychology, biology and physics. Field research uses methods from sociology and anthropology. There are plenty of textbooks on research methods in these fields, and we won't attempt to summarize them here.
What's special about parapsychology is the need to pay very close attention to "conventional" explanations. This is because we've defined psi phenomena as exchanges of information that do not involve currently known (i.e., conventional) processes. For instance, we talk about "ESP" when people know about things going on in their environment without getting the information by seeing, hearing, touching, smelling, or through any other known sensory input, or without being able to figure out the "target" information. We talk about "PK" when physical systems appear to react to people's intentions and there's no known physical contact between the person and the "target." Words like "without," and phrases like "no known," show up a great deal in descriptions of psi phenomena.
Therefore, an important part of parapsychological research is eliminating known contact methods from laboratory setups and thinking carefully about them when evaluating reports of people's experiences. In ESP research, this requires knowing about the psychology of sensation, perception, memory, thinking, and communication, and about the biology and physics of sensation and movement. In PK studies, it is important to know about the physical characteristics of the "target," how it works, and what might affect it. In field studies, and in most laboratory studies, it's important to know about the ways in which people can interact with each other. Of course, in field studies it is much more difficult to eliminate conventional explanations than it is in the laboratory because you can't set things up beforehand to eliminate conventional contact between the people and the "targets."
Even when known contact methods are well controlled or eliminated, there is always the possibility that what we observe could have occurred by chance. That is, a person's apparent ESP knowledge about some distant event might be a random guess that just happens to resemble the target. Or, what looks like a PK effect on a physical system might be a random change in that system that just happens to occur at the right time. So it's important to know the statistical methods used to measure how likely it is that the event could have occurred by chance, and how to decide when that's so unlikely that it makes more sense to think there really was some kind of psi contact.
Sometimes field research is not concerned with whether the experiences people report were really psi phenomena, but instead asks questions like, "What do people report about experiences they think were psi?", "How does having these experiences affect their lives?", and "Do people's psychological or cultural characteristics influence how likely they are to interpret experiences as psi?" This is straightforward anthropological, sociological, or psychological research and does not require the same kind of strict attention to eliminating conventional explanations. The value of field research methods is that they investigate the experiences that people actually report. These include experiences such as precognitive dreams, out-of-body experiences, telepathic impressions, auras, memories of previous lives, hauntings and poltergeists and apparitions. Research on these issues results in information about incidence, phenomenology, demographic and psychological correlates of the experiences.
While field or spontaneous case research is less technical, and often more exciting to read, it is wise to avoid jumping to conclusions about the nature of psi from individual cases. Such studies examine how people report or think about their experiences, not what those experiences actually are. However, because spontaneous case studies concentrate on the "raw experience," they offer a valuable view of psi that is often missing in controlled laboratory experiments. Case studies provide a chance to discover the personal meanings and the psychodynamics underlying the experiences, which in turn may provide important hints as to possible mechanisms of psi.
An important goal of laboratory research is to determine the degree to which experiences reported in field and spontaneous-case research can be verified using current scientific methods. If they prove to be verifiable in the lab, the major intent of the lab work usually shifts from "proof-oriented" research to "process-oriented," in which the goal is to discover the psychological, physiological, and physical mechanisms of each phenomenon.