How to get a Japanese driver's license
Anyway, for those of us who are from a civilized part of the world, it's actually a very simple task! You will need to prepare five things: Your valid driver's license from your home country, a certified translation of your driver's license, a photo, money, and a passport that shows (through the universally accepted cryptographically secure method of embarkation/disembarkation stamps) that you've lived in your home country for at least three months since acquiring your driver's license. Let's go through these in detail.

1. Valid driver's license
From your home country. I don't know what happens if your driver's license is from a country other than that of which you are a citizen. It'll probably be trouble.
2. Certified translation of your driver's license
You can get this at your country's embassy in Japan. For Swedes, this translation service is available on Monday mornings, and costs 2,400 yen. They translate your driver's license and give you a paper certifying the authenticity of the translation.
3. Driver's license-sized photo 30x24 mm. Photo booths in Japan have an option for this size called "driver's license", or something. Interestingly, this photo is used for your application only, i.e. not on the driver's license itself, so it doesn't matter if you look like a dork in it (you don't look like a dork anyway, do you?). They'll take the photo for the actual driver's license for you at the driver's license office.
4. Money
It costs 4,500 yen. No so bad... You trade the money in for the equivalent in stamps at a place in the license office that sells stamps, as is common in Japanese bureaucracy.
5. Passport
You need a passport that shows you've been living (or at least being) in your home country (which we're assuming is also the country that issued your driver's license) for at least three months since the date when you acquired your driver's license. If you haven't been living there for three months, you can't switch to a Japanese driver's license. This is presumably to ensure that people don't just run off to some other country where it's cheaper and easier to get a driver's license.
If you can show you've been living in your home country for at least one year since acquiring your driver's license, you'll be exempt from the one-year newbie period (which means mostly that you have to have silly stickers at the front and back of the car while you're driving).
The procedure
Go to one of the driver's license offices. There are three Driving License Testing and Issuing Centers in Tokyo, in Shinagawa-ku, Koto-ku, and Fuchu-shi. You can find the addresses, as well as some sparse information, on this page. For other prefectures, you'll have to google it yourself. I went to the one in Fuchu, which can be reached by bus 91 from Chofu (Keio line), or by bus from Tama-reien station (also Keio) or Koganei station (on the Chuo line). The bus stop is called, revealingly, Shikenjo Seimon (試験場正門). They have lunch breaks so get there early.
Find the counter for changing a foreign driver's license to a Japanese driver's license. Look for the word 切り替え/切替 kirikae. It's probably close, or the same as, the counter for international driver's licenses. But you don't want one of those. In the Fuchu office, it counter number 31 on the 3rd floor. Once there, present all your prepared materials at the counter. They will then take some time to examine your papers and make sure you've lived in your home country for the required amount of time since acquiring your driver's license, etc.
Actually, from there they were very helpful and provided quite clear instructions on what to do (in Japanese). You'll have to go buy a stamp, as mentioned above, and take an eye-test, which takes about 30 seconds and you'll invariably pass it, take a photo for the actual driver's license, and then input two 4-digit pin codes into a machine (smeg knows what they're for). That whole procedure took about 5 minutes.
All of this took about one hour to complete. One of the few non-unpleasant encounters I've had with Japanese bureaucracy. Then you're done, but I had to wait one and a half hour for the actual driver's license card, which you can pick up at an adjacent office. So two and a half hours in total, from arriving at the office until having the license in my hand. Sweet.

