Japanese tend to be shy, but are usually delighted if you show them genuine friendship. Many are looking for direction in life, and once they trust you, may be keen to hear your testimony or learn about Christianity. But be patient, it can take them time to come to faith.
Here are some ideas you could try:
invite them over for a meal
go out for coffee
take them to a local place of interest or out into the countryside
help them in practical ways (filling in official forms etc.)
share your testimony—tell them what Jesus has done in your life, how God helps you day-to-day etc.
invite them to church (Christmas and Easter are good)
offer to read the Bible with them in English
introduce them to Japanese Christians or local Christians who have lived in Japan.
give them a Bible (preferably bilingual, and encourage them to read in both languages)