Dokusan (独参) is a formal meeting with a Zen teacher, typically a priest who has received Dharma Transmission from their own master. The point of dokusan for the student is to get instruction on how to move forward with their practice, how to keep progressing towards, well, nothing.
I scheduled a meeting after my first one-day sit, because I had some questions about my experience and wanted to know what steps to take next. That meeting was at 6:30 in the morning at Green Gulch—apparently you have to get up early to catch a zen master—so I booked a room overnight, got up at 4:30 for the first siting period in the zendo, left at the first walking break and wandered around in the misty foggy morning for a few minutes before the appointed time.
What goes on in a dokusan meeting is private, variable to the student's needs, and for an outside observer probably not that interesting. What is interesting are the forms for a teacher interview, which vary from temple to temple, even in Japan. I did some reading ahead of time and found the following in D. T. Suzuki's, An Introduction to Zen Buddhism:
…seeing the master does not take place openly; the monk is required to go individually to the master's room, where the interview takes place in a most formal and solemn manner. When the monk is about to cross the threshold, he makes three bows, each time prostrating himself on the floor; he now enters the room keeping his hands palm to palm in front of his chest, and when he comes near the master he kneels down and makes still another prostration.
This ceremony over, no further worldly considerations are entertained; if necessary from the Zen point of view, even blows may be exchanged.
D. T. Suzuki was principally concerned with Rinzai Zen, which differs in it's forms from Soto Zen as practiced at the Zen Center. Fortunately there is an excellent description of the forms for dokusan as imparted by Shunryu Suzuki in Crooked Cucumber:
[Suzuki Roshi] gave dokusan in the congregation's office at the bottom of the stair. When it was Betty's turn for dokusan, she sat zazen in the hall until she heard Suzuki's handbell ringing to announce that it was her turn. She fluffed her cusion, bowed, and slowly walked into the office. There Suzuki sat on a zafu facing an empty zafu a few feet in front of him. Behind him was a little altar that had been set up for the dokusan, with a candle that provided most of the light in the room. Following the procedure Suzuki had taught them, Betty bowed upon entering the room and did three full bows [prostrations] before Suzuki.
Similar, but there are some differences, the number of bows, the use of the bell, when to gassho, etc.. Of course, all that reading left me somewhat over-prepared. The forms for my teacher meeting were abbreviated versions, I was ready to prostrate myself but only bell ringing and gassho bows were required.
However, the fundimental form of teacher and student meeting face to face is unchanged. The heart of the process is the same and the forms are only there to create the right atmosphere. The forms of Zen are empty of meaning but critical to set the stage and prepare the mind, they exist to create a situation where you are bound to make mistakes, where you are forced over and over to retreat to your beginners mind.
Like the precepts, forms are made to be broken, they represent a goal which is impossible to attain but which we can always aspire to. To quote Suzuki Roshi:
"Every thing you do is right, nothing you do is wrong, yet you must still make ceaseless effort.