I get a lot of questions about the possibility of getting training in Singapore Math. The answer depends on what you are interested to do and which country you are in.
If you are interested in graduate studies, NIE offers masters degree in many specialization, including mathematics education, primary education and secondary education (there are many other fields of specialization). We have foreign stduents who complete the course full-time in a year although a year and a half is not so tight. NIE has both coursework as well as coursework plus thesis option.
If you are interested in Ph.D., you need to be here in the initial part to complete your coursework and to work out your research problem with your supervisor. You may do the research here or in your home country. You will be expected to be back here in Singapore towards the end of the candidature and for your oral examination before the degree is conferred. If you are interested please email me firstname.lastname@example.org I can link you up with potential supervisors.
If you are more interested in getting training for classroom teaching rather than graduate degrees these are some options.
Join NIE's post graduate diploma in education (PGDE Primary) where you get pre-service training in two or three subject areas including mathematics teaching. It is one year. If you are not interested in the diploma and just want to focus on mathematics then I think there is an arrangement for you to do this as a non-graduating student.
Join NIE's inservice course. There is a range of subjects available throughout the year. From lesson study to problem solving to action research. A 12-hour course runs over 4 weeks. (once a week).
In some countries, there are institutes already in place. In the US, there is a summer institute every year. Go to http://www.sde.com/conferences/singapore-math/index.asp for details.
Some school districts run theirs. I have been to Scarsdale School District twice to teach a course in their own teacher institute. I believe in the last course there were teachers not from the school district who joined the course.
In places like the Philippines, Indonesia and Chile, the book distributors have been organising training seminars at least once a year.
If you are thinking of running such institutes in your country, I can put you in charge with the book publisher to explore this possibility.