During a Testing Dojo, each person in the room fills one role. There is of course the role of the tester who has the power over the keyboard who interacts with the software. Then there is the recorder's role, which takes session notes and makes sure to get reproducible steps noted down. The observer watches the performance. He thinks about suggestions for improvements and gives observations about communication in a paired setup. Finally, the facilitator makes sure that the rules of the dojo are followed.
As the tester has the control over the keyboard, he interacts with the program. It's crucial for the tester to expose his testing ideas about what to try or not to try and describe his mental model to the audience.
The recorder takes session notes about the activities. In a single tester setup the tester is simultaneously the recorder and he has to take care about his own session notes. In a paired setup there is a dedicated person for this.
In a Testing Dojo there are one or more observers, depending on the size of the group. The observers takes notes about the process. These notes include the interactions between tester and recorder in a paired setup or spoken thoughts and test activities in a single setup. Observers should monitor the testing activities and the interactions between the pair, rather than watch the screen. Additionally, observers should try to keep track of one or two points, rather than trying to observe everything. If you are neither testing nor recording, you are not taking a break. As an observer you have the responsibility to stay engaged and follow what happens.
Specific things to observe might be test heuristics, test framing, oracles, coverage ideas, management of focus, conversation, monologues, pauses in talk, pauses in testing, eye contact. The facilitator might want to hand out some common oracles or mnemonics for the participants.
The facilitator picks the mission for the dojo. She enforces the rules like switching timeframes. At the end she moderates the feedback activity. The facilitator could also take on the role of the tester, recorder or observer, but her main responsibility is to facilitate the dojo. A junior tester can take on the role of the facilitator in order to learn the skills to lead a group or meeting.