For most people, the idea room for practicing Tai Chi is around 8 meters x 3 meters. However, you can practice Tai Chi in smaller spaces too. If you are a bigger and/or taller person you might need a little more room to practice in.
On your first Tai Chi class you should receive a formal introduction to Tai Chi followed by basic guided warm ups or stretches. You should enjoy a place of quiet, and together with a group of people (possibly also on their first Tai Chi class) learn the first moves by repeating after your instructor.