The tea ceremony is one of the most important tasks you must perform as a Ninja. It is a test of your knowledge and competence in Agatean culture. Also, the cunning ninja may use the tea ceremony to inhume certain targets. I won't describe the steps necessary to perform the ceremony as they are very clearly described in the tea ceremony room where you will also find Tu For Teeh.
If you are having trouble, ask an experienced Ninja to demonstrate. If no one is available, be sure to look at the utensils available to you and use the "syntax" command to help discover the correct steps.
Note that to practice poisoning the tea with Tu For Teeh you do not need to have any actual poison with you.
Successfully completing the tea ceremony awards the title Chojin.