Japanese law states the following conditions:

1. Continuous residence in Japan for five years or more
• Translation: You have to have legally lived in Japan under some kind of normal visa for five years or more, even after subtracting out the time you have been overseas for vacations, business trips, etc.  "Normal Visa" means work visa, student visa, etc.  Tourist Visas, Diplomatic Visas, etc., do not count.  Also, if you completely cancelled your visa status and then re-enrolled, then you can't count the period from your previous visa.  If you simply renew your visa every time it expires (before it expires!), then it does count.
2. At least 21 years old and otherwise legally competent
• Be old enough, and don't have any severe mental illnesses, etc. that would prevent you from knowing what you are doing.
3. History of good behavior generally, and no past history of seditious behavior
• In practical terms, the case workers can reject you for any reason they see fit.  This item basically means "pay your taxes" and "don't commit crimes".  If they see you are a member of a cult or anarchist group, or are generally running around causing trouble, they will reject you.
4. Sufficient capital or skills, either personally or within family, to support oneself
• This basically means you should have a college degree and a reasonable job - or have enough money saved up to not need a job.  You don't have to be super rich, though.
5. Stateless or willing to renounce foreign citizenship
• Japan does not officially allow dual nationality, so you have to give up your other passport.  For countries like China, this is enforced, and you must renounce your other nationality and cancel your passport before officially applying for Japanese citizenship.  For other countries like the Unites States, you are supposed to cancel your old citizenship within 2 years of obtaining your Japanese citizenship - but there is from all accounts a kind of "don't ask don't tell" policy.  There have been various rumblings about changing the official policy to allow dual nationality, but nothing has been passed into law at this point.