If you are studying with a tourist (tanki-taizai) visa, then you are not allowed to work. It is illegal to work in Japan without an appropriate visa. You will need, as a minimum, a student visa if you plan to work.
Student visa holders (Shibuya Campus only) are allowed to work subject to certain conditions once permission has been obtained in the form of a document from the Immigration Bureau. Most long term students do seek part time work, partly to support finances, and partly for the cultural experience of interacting with native speakers of Japanese outside the classroom. You are allowed to work up to 28 hours per week, and up to 4 hours per day, but we recommend not working more than about 12-15 hours per week, as it can have a detrimental effect on your studies.
When seeking work, searching the internet helps, but so does word of mouth. Tokyo is the easiest city in Japan for students seeking part time employment.
If you have any doubt about visa status, please feel free to contact us.