I've been studying the Urasenke Way of Tea (one of the largest schools of Japanese Tea) for over 5 years, I can answer your questions from that school's point of view.
I've talked about this before, you might be able to find the thread searching about tea on this website.
Also, you can take a peek at the Urasenke home page (it has English) at:
Because the previous Grand Master made it his life's work to spread "peacefulness through a bowl of tea", many school chapters can be found throughout the world. Those chapters give lessons, of course, and often do demonstrations at Japanese festivals, museums, and other events. You can probably find out more information by contacting the London headquarters at:
4 Langton Way
tel: 44 (20) 8853-2595
fax: 44 (20) 8293-4088
Although it's commonly referred to in English as "Tea Ceremony", the two words for it in Japanese are "Chanoyu" (Hot Water for Tea) or "Sado/Chado" (the Way of Tea). Although the Way of Tea involves philosophies and traditions from Buddhism, Christianity, Shinto and other religions, it is not a religious ceremony. It is more about appreciating the moments you have together as guest and host.
At the international school at Urasenke, students from around the world study together. When I visited, there were students from China, Korea, Germany, Finland, Egypt, Canada, the U.S., Brazil, and England, among others.
Your question is actually a lot more complicated than is easy to answer here, but I will try...hope you don't get bored.
On what occasions....?
First of all, although many people study tea in Japan, not many people actually get a chance to host a tea. Not very many people have a tea house or room at their home, so, outside of lessons/practise, they may only have a chance to attend a "real" tea a few times a year at most, if at all. Often these are sponsored by their local chapter and are big tea events called "chakai" (tea meetings). In this case, hundreds of people may attend. The host makes tea in front of all the guests, but s/he (nowadays mostly women study tea, even though it used to only be men over a hundred years ago) only makes the first few bowls for the first few guests. The rest are made in a back room and brought out to the guests by assistants. Some public schools offer tea as a club activity, too. The four Principles of Tea are Harmony, Respect, Purity, and Tranquility. Therefore, guests and host learn a lot about manners and how to make sure that the guest is as comfortable and well-taken-care of in the tearoom. Some people think of tea classes as something that teaches children (who are in club) or young women proper manners and etiquette.
True tea rooms are as small as 2 tatami mats and as large as 8. Typically there are only 3-5 guests invited. A host can invite guests for any particular reason;
The most common reason is the last tea of the year and the first tea of the new year, in which they might have a whole meal along with their tea.
Perhaps it is in honor of the first guest for some reason (birthday of a person who especially likes tea, for example) or because the snow is beautiful, or it is a full moon in fall. Or, students have a tea to commemorate a special occasion. In March, Urasenke students play a tea game to commemorate Sen Rikyu, one of the people who was most influential in developing the Way of Tea over four hundred years ago.
What do we do at tea? Well, what procedure, utensils, decorations, and so on are determined not only by the hosts' taste, but the occasion and season as well.
For example, especially for the host, every movement is taught in the preparation of the tea. This is to ensure the most beautiful and practical presentation. However, the placement of utensils, such as the kettle, moves during the year (in the hot summer, the kettle is moved as far as possible from the guests, and in the winter, as close as possible). So, then we have to learn all the procedures for the different seasons. Or we have to learn procedures if there is a shelf to hold the utensils, or depending on the formality of the occasion, or depending on the kind of utensils we use. It becomes a lifelong practise because at the same time we are learning all these procedures, we are also learning about all the arts that go along with the tea room and procedures. We learn about ceramics, flower arrangement, kimono, calligraphy, incense, lacquerware, textiles, and on and on, because the guest might ask about them and how they are incorporated into the tea. And, it makes the study all-encompassing and applicable to daily life.
At a tea, guests walk through an outer garden into an inner garden. There they will find a bench to wait until they hear the signal to come into the tearoom. Then they will rinse their hands and mouth at the tsukubai, or a kind of fountain, and enter through a tiny door that forces them to bow low on their knees to come in (this enforces the feeling of equal humility among the guests). They go to the tearooms alcove and admire the scroll and the flower arrangement, and also go to the kettle and admire the way the charcoal and ash have been arranged. They do this one by one, always politely saying things like "excuse me for going ahead of you" to each other.
Once they are seated, the host begins by bringing in the sweets for the guests and then s/he brings in the utensils and begins. The room is very quiet until the first guest has had his/her tea. Then s/he may ask the host questions about the tea or sweets or scroll until s/he hears the last guest's last sip. Since everyone is supposed to forget about their worldly cares, the conversation only sticks to the tearoom and utensils. That way, there is no disharmony brought up by politics or subjects that may disturb anyone else in the tearoom.
It is a very quiet, tranquil experience, and since everyone is supposed to forget about anything in the outside world and enjoy this moment together, most people feel very calm and connected with the people they share the experience with.
I hope you get a chance to see a tea sometime. It's a difficult question to answer, but if you connect to that teahyakka website, you can get much more concrete information, and maybe you can sit in on a lesson or demonstration!