Generally a PG degree is required for enrolling in PhD which is supposed to be over by 3 years. However some institutions in Japan and South Korea take graduate students directly for a 4 year PhD plan. If you want to do it from some institute in Japan or South Korea then there are two ways to approach the issue.
First one is you explain your desire to do PhD from abroad to some senior faculty in your University or institution under whom people are already doing PhD. Take his guidance and help in preparing a base document for your proposed research work and indicate the potential studies you will be carrying there to pursue your research work. Once this white paper of your proposed research work is prepared you submit it to the institutes in those countries for their consideration whether they can accommodate you there in the coming academics years. They will be asking you some questions regarding your proposed stay there as well as your financial condition to afford that work there.
If your proposal has an upside potential you may even receive sponsorship or scholarship for your project as in many countries there are some such financial aids for developing countries.
The second approach is that you can directly apply for PhD in that particular institute and give all your details and educational credentials and source of finance for your stay and studies there.
Depending upon your qualifications they may call you to join for it. In few cases they may ask you to go through a one year pre-qualification course and pass it successfully before starting your PhD there. The reason for this is basically to keep a quality control on the work carried out by PhD aspirants.
In Japan, there are hundreds of universities and most of them are autonomous or private. The Govt of Japan is encouraging foreign students to take education from there. So there is a conducive environment to that extent. Many universities in Japan take an entrance test for admission to PhD or alternately you have to produce a GRE score.
Some of the top universities in Japan are -
University of Tokyo, Kyoto University, Osaka University, Tohoku University, Tokyo Institute of Technology, Nagoya University, Kyushu University and Hokkaido University.
In South Korea also there are many universities enrolling foreign students for PhD and an average period is 3 years including assessment examination and submission of thesis. South Korea is well advanced in the area of science and technology and more PhD options are there in that field only. However some institutes offer PhD opportunities in humanities also.
Some of the good universities in South Korea where PhD can be pursued are -
Korea Advanced Institute of Science and Technology (public), Pohang University of Science and Technology (private), Yonsei University (private) and Korea University (private).
Knowledge is power.