One of the things you will have to come to terms with when you move to Japan is that housing here is just not the same as your home country. If you come from a western country like Canada, you have the luxury of insulation. Even in apartment buildings, while it is possible to hear the occasional bangs from upstairs, your neighbour would often have to really make a huge effort to make that noise in order for you to hear it. At least, that's how my apartment in Toronto was.
In Japan, not only is insulation not really a thing, you will most likely be dealing with your neighbour's noise at some point.
Walls here between apartment flats are just so, so thin.
I currently share a wall with one next door neighbour. The wall between his apartment and mine are literally the same material as being an adjacent bedroom next to your parents' or your siblings'. At least it feels like it...
If my neighbour spoke in a normal volume, you can hear him.
Yes, it would do me good to find a new apartment that has better walls - but here's the thing. Many Japanese apartments really DON'T have better walls. If they do, they are often older buildings, out of my price range, or they aren't apartment available to foreigners.
So, in essence. It is quite unavoidable.
In Japan, you often just have to suck it up. If day time noise is really a bother, then you really need to make an effort to find the apartment and maybe be more willing to give up some needs/wants for it.
However, if the noise happens at night (around midnight or some other), you may have more recourse. I have called the police on my neighbour several times during the hours between 1AM to 4AM. Each time, the police came. Here's my experience:
I called the emergency number and spoke in Japanese to the police officer on the phone, telling them that I was able to hear my neighbour next door, talking or some other very loudly. I told them I wasn't too sure. They'd then proceed to ask for my address if they don't have any other follow up questions (sometimes they might ask how long it's been happening, etc). They also asked for my name, and my nationality since my name is not Japanese. A fair question, I think. Nothing xenophobic about it, as I've never gotten comments about it after.
Afterwards, they'd ask if my apartment has an auto-lock system in the lobby. If you did, you'd be asked if it's ok to buzz your unit to get inside. The police won't actually go to your apartment at all, they will go straight to the door of your noisy neighbour. They will also not tell your neighbour who has called.
Usually it doesn't amount to much.
If your neighbour has some sense to open the door, the police will chat with him or her. Then off they go. Hopefully your neighbour also has some sense to shut up since police had just shown up at their door. If they don't... well.
You can also try to call your management company and complain through them. Again, it doesn't amount to much. They will probably just tell you to call the police in the end. Mine has offered to print out notices to send to other tenants to basically tell people to stfu at night, but you can gauge the effective of that if your neighbour really just don't give a fuck to begin with.
I don't advise approaching your neighbour by yourself. If things get hostile for you and the police are called, there's a high chance that you as the foreigner will be at a huge disadvantage over your neighbour who is Japanese. Your hostile neighbour may also end up escalating the noise because they now know it's YOU who is complaining about them.
In conclusion, basically... there's not much you can do about a noisy neighbour. You can only hope that the police scares them and they have some form of curtesy to not be loud during sleep hours.