Here's an overview:
Duration: up to 3 months
Amount: as much as 60% of your average previous paycheck per month
Requirements: have a work visa, have been paying employment insurance (usually automatically deducted from your wages) and be able to prove you are unemployed and actively looking for work.
"actively looking" means completing two documentable tasks each month (such as going into the Hello Work office and putting together a CV).
The place to go to sign up for this is ハローワーク (Hello Work). You won't find any English assistance on the website (branch locator is here), and may not in person, either, in small cities.
Further details (in Japanese) can be found on this employment insurance webpage.