Teaching Chinese language usually involves Mandarin, the standard official dialect. However, I have actually had more clients who are interested in Cantonese than Mandarin, and for a variety of reasons (some professional, others personal). Below is my pedagogy for teaching Chinese dialects:
In teaching Chinese dialects, I have discovered a very effective way for teaching Cantonese to non-Cantonese Chinese students, whether they are from mainland China, Taiwan, Singapore or anywhere in the modern Sinosphere, and that is Chinese dialectal correspondences. This is based on my teaching methodology of tailoring the foreign (target) language to my students' mother (base) language, and in the case of Chinese speakers, assuming that they know modern standard Mandarin (the lingua franca in the Sinitic world), it is very helpful to apply the Comparative Method and reconstruct proto-Chinese and dialectal correspondences, which allows them to relate Cantonese (or any other Chinese dialect) to their mother tongue and imply memorise the similarities/differences. More on this in due course.
It has been fascinating applying the traditional Comparative Method which I learnt in my study of Indo-European and classical philology at the University of Oxford to my native Chinese dialects, which has worked well for Chinese learners of Cantonese. This is a good example of how my knowledge and expertise in theoretical linguistics has aided my work in applied linguistics. Please note that with non-Chinese students of Cantonese (or Mandarin), I would never use this method since they do not have this linguistic base (Chinese), in which case I would always teach them grammar from scratch, which has also been very effective, as seen in my students' feedback forms.