In Tokyo, taxi cabs cruise around the
streets looking for people to pick up. So all you need to do is
stand close to the street, look for an unoccupied car,
and wave your arm around a bit. If the
taxi driver sees you, he (for it is almost always
a he) will often turn on the hazard
warning lights and steer towards you. When the cab
gets up to you, the rear left door (the
one facing the sidewalk, since Japan drives on the left)
will open automatically by hydraulics.
You get in, and when everyone's safely inside the
car, the door closes automatically. Same for
when you get off. Thus, you never need to bother opening/closing
the rear door.
In Tokyo, if you turn on your hazard
lights you're allowed to do anything, break any
traffic rule, block traffic, and just be generally completely
irresponsible. So don't worry if you hail a car that is far away
and needs to cross a large number of high-traffic lanes, including
bus-only lanes and pedestrian lanes, to get to where you are - for
he'll do it. The same is true for when getting off.