The problem with teaching introspection is that you may only be teaching the subject to experience what you expect them to experience. Psychologists in the late 1800's and early 1900's tried to develop protocols where experimental subjects were taught how to report the contents of their consciousness, but this was not very successful. The results of a lab using a specific introspection protocol could not be easily replicated in a lab using another protocol, IIRC. Even having the subjects simply report their experience with no interpretation at all is difficult:

It was never wholly true that introspection was photographic and not elaborated by inferences or meanings. Reference to typical introspective researches from Titchener's laboratory establishes this point (28, 58, 25, 64, 59, 16, 31). There was too much dependence upon retrospection. It could take twenty minutes to describe the conscious content of a second and a half and at the end of that period the observer was cudgeling his brain to recall what had actually happened more than a thousand seconds ago, relying, of course, on inference. At the Yale meeting of the APA in 1913, J. W. Baird with great enthusiasm arranged for a public demonstration of introspection with the trained observers from his laboratory at Clark, but the performance was not impressive. Introspection with inference and meaning left out as much as possible becomes a dull taxonomic account of sensory events which, since they suggest almost no functional value for the organism, are peculiarly uninteresting to the American scientific temper.

Classical introspection, it seems to me, went out of style after Titchener's death (1927) because it had demonstrated no functional use and therefore seemed dull, and also because it was unreliable. Laboratory atmosphere crept into the descriptions, and it was not possible to verify, from one laboratory to another, the introspective accounts of the consciousnesses of action, feeling, choice, and judgment. It is not surprising, therefore, that Killpe, Watson and Wertheimer, all within a decade (1904-1913), reacted vigorously against the constraints of this idealistic but rigid pedantry.

On the other hand, modified introspective methods have been making somewhat of a comeback recently:

In no period, however, were introspective methods entirely abandoned by psychologists, and in the last few decades, they have begun to make something of a comeback, especially with the rise of the interdisciplinary field of “consciousness studies” (see, e.g., Jack and Roepstorff, eds., 2003, 2004). Ericsson and Simon (1984/1993; to be discussed further in Section 4.2.3 below) have advocated the use of “think-aloud protocols” and immediately retrospective reports in the study of problem solving. Other researchers have emphasized introspective methods in the study of imagery (Marks 1985; Kosslyn, Reisbert, and Behrmann 2006) and emotion (Lambie and Marcel 2002; Barrett et al. 2007).

Beeper methodologies have been developed to facilitate immediate retrospection, especially by Hurlburt (1990; Hurlburt and Heavey 2006; Hurlburt and Schwitzgebel 2007) and Csikszentmihalyi (Larson and Csikszentmihalyi 1983; Hektner, Schmidt, and Csikszentmihalyi 2007). Traditional immediately retrospective methods required the introspective observer in the laboratory somehow to intentionally refrain from introspecting the target experience as it occurs, arguably a difficult task. Hurlburt and Csikszentmihalyi, in contrast, give participants beepers to wear during ordinary, everyday activity. The beepers are timed to sound only at long intervals, surprising participants and triggering an immediately retrospective assessment of their “inner experience”, emotion, or thoughts in the moment before the beep.

Introspective or subjective reports of conscious experience have also played an important role in the search for the “neural correlates of consciousness”; (as reviewed in Rees and Frith 2007; see also Varela 1996). One paradigm is for researchers to present ambiguous sensory stimuli, holding them constant over an extended period, noting what neural changes correlate with changes in subjective reports of experience. For example, in “binocular rivalry” methods, two different images (e.g., a face and a house) are presented, one to each eye. Participants typically say that only one image is visible at a time, with the visible image switching every few seconds. In “early” visual areas—that is, brain areas relatively early in the flow of visual processing (such as V1)—researchers tend to find evidence that both images are being processed and changes in neural activity tend not to be temporally coupled with reported changes in visual experience. In contrast, in areas further downstream—such as frontal and parietal areas—changes in neural activity do appear to be temporally associated with reported changes in conscious experience (Lumer, Friston, and Rees 1998; Tong et al. 1998; Kreiman, Fried, and Koch 2002 Moutoussis and Zeki 2002; Tong, Meng, and Blake 2006; though see Polonsky et al. 2000), and so also, perhaps, are large-scale changes in neural synchronization or oscillation (Tononi et al. 1998; though see Kamphuisen, Bauer, and van Ee 2008). Another version of the ambiguous sensory stimuli paradigm involves presenting the subject with an ambiguous figure such as the Rubin faces-vase figure. Using this paradigm, researchers have found neuronal changes both in early visual areas and in later areas, as well as changes in widespread neuronal synchrony, that correspond temporally with subjective reports of flipping between one way and another of seeing the ambiguous figure (Kleinschmidt et al. 1998; Rodriguez et al. 1999; Ilg et al. 2008; Parkkonen et al. 2008). In masking paradigms, stimuli are briefly presented then followed by a “mask”. On some trials, subjects report seeing the stimuli, while on others they don't. In trials in which the subject reports that stimulus was visually experienced, researchers have tended to find higher levels of activity through at least some of the downstream visual pathways as well as spontaneous electrical oscillations near 40 Hz (Dehaene et al. 2001; Summerfield, Jack, and Burgess 2002; Del Cul, Baillet, and Dehaene 2007; Quiroga et al. 2008). However, the proper interpretation of these results remains contentious (Noë and Thompson 2004; Overgaard, Sandberg, and Jensen 2008; Tononi and Koch 2008).