The European participants need to apply through Horizon 2020 while the participants in Japan apply through the corresponding programme in Japan. A coordinator needs to be identified on both the EU and the Japanese side. Between those two, a coordination agreement should be concluded. There is a check list for this agreement available on the Horizon 2020 Participant Portal. The list that has been used previously is the following, please check whether it is still valid for the call you are applying to: https://ec.europa.eu/research/participants/portal/doc/call/h2020/h2020-euj-2014/1592603-checklist-coordination-agreement_h2020-v1_en.pdf
Please note the above information was valid for the MIC/NICT coordinated call in 2016. The procedure could be different in the future.