Japanese Olympian

How would a gaijin get on the Japanese Olympic Team? And how could they afford it?

Hopeful,

How would a gaijin get on the Japanese Olympic Team?

By becoming Japanese.

i.e. many years of residence in Japan would be necessary.

Nationality is the least of your worries, you'd need to be
better then the Japanese themselves at whatever sport you played.
I'm sure once you can show that (Impressing coaches and whatever), they'll pull some strings at the governmental level.

Realistically speaking, being on the Olympic team is hard even for the regular person, yet alone someone not from the country.

Certainly plenty of sports people have been fast-tracked to citizenship. You would have to really excel and preferably already be known in your home country as a star in that sport though, which makes me want to ask, why not become an Olympian for your own country?

personally i hate my home country and wouldn't want to represent it for personal reasons.

but as others have mentioned there are 130million or so people in japan and any one of them could be an athlete competing to be an olympian. plus if you're over 20 your odds of being skimmed over in favor of somebody younger are pretty high for most sports.