[Nyororin]

From my understanding, there are several ways to handle your taxes. You can pay it yourself at town hall in a lump sum each year, pay it in a set of installments yourself, or let your company take care of it.

Most people let their company take care of it, and have so much extracted from their pay each month (including the first year). The company does the paperwork and pays in April.

It sounds like your friend is paying his taxes himself - this is pretty common when someone starts out freelancing or with work split between multiple companies. The catch is, however, that while it feels like you pay no taxes the first year... You can forget and end up having a year due after losing your job, like what has happened to your friend.

For shorter term stays in Japan (English teaching), companies are very careful to take more than enough from the paycheck as an employee that has left the company will have basically left them with the bill.

I imagine there are some people out there who take a bit out each month and set it aside to pay for their taxes in April, but I would say that most people either let their company do that or pay in a flat fee come April.
As an example, my husband's company takes out a flat amount from his paycheck each month to cover taxes. I, on the other hand, am freelance - so file my taxes myself and pay the bill in segments.