Hello Work
http://www.hellowork.go.jp/
This is a government-run employment program that serves mostly Japanese but also helps foreigners. This is probably the first place you should go. If you need translation, make an appointment ASAP. They don't have an English website that I've found but a list of offices with limited English support can be found here. As of this time, I know for sure that at least Shinjuku provides English services.
Tokyo Employment Service Center for Foriegners
Roppongi Job Park 3F, 3-2-21 Roppongi, Minato-ku, Tokyo 106-0032
Tel: 03-3586-8609 Fax: 03-3589-8670
E-mail: tfemploy@mb.infoweb.ne.jp
http://www.tfemploy.go.jp/
I went here by accident when looking for Hello Work. It's used more by people without valid working visas and most kinds of students. Chinese and English service always available. The English section of their site appears to be down.
Career Cross
www.careercross.com/en
A website providing information on bilingual jobs. Some monolingual jobs also posted. This is one of the more up-to-date and reliable online resources I've used.
Japan Times Jobs
www.job.japantimes.com/index_e.php
Another reliable online resource for jobs. It's updated at least every Monday. Most positions posted here are for mid-career job seekers.
Gaijinpot Jobs
http://www.jobs.gaijinpot.com/
During my fist visit to Tokyo this was my go-to site for employment. It posts mostly English teaching jobs.