How to turn right in Japan
According to this Tokyo Metro Police Department (警視庁 Keishichō) web page on bicycle rules, the pet peeve of the authorities in Japan with regard to right turning cyclists is the practice of just going like cars through the turn.

Three cases are specified, which all share the common theme that the cyclist, second class creature that it is, must turn right by crossing the intersection twice, like a lowly pedestrian, and not like a vehicle.



The diagrams are self-explanatory.


At an intersection with no signals, look both ways, and proceed straight through. As you approach the other side, then turn right and cross again.
At an intersection with signals, but no pedestrian/cyclist signals, proceed through the intersection (and swerve a bit toward the pedestrian crossing, according to the diagram). The accompanying text says you should walk your bicycle if the crossing is busy with pedestrians. Then wait, on the road, for the signal to change for the second crossing and then proceed, similarly to a vehicle (away from pedestrians).
At an intersection with pedestrian/cyclist signals, cyclists are expected to similarly cross twice, obeying those special signals, sticking to the bicycle section of the crossing.  The main difference is that waiting for the second crossing is done off-road, and then the crossing is carried like the first, with the pedestrians.


It's not clear whether the page incorporates any 2015 changes in rules, but it was modified in April 2015.

The very last diagram makes it clear that bicycles are not to behave like motor vehicles. They should stick to the left. Even if there is a left-turning lane and they wish to go straight through the intersection, they must do so from that left-turning lane, and not from the adjacent lane which goes straight. Likewise, they must not occupy the right lane (from which it would be possible to turn right like a motor vehicle).