O-rei is money or presents given in return for a favour. Usually, it refers to money. There are many occasions in which O-rei should be given. For example, when attending a chakai, when attending keiko with a teacher other than your normal one, or after receiving a present.
O-rei should be given wrapped in paper or in an envelope. Real mizuhiki and a paper noshi or an envelope printed with mizuhiki and noshi on it should be used. Above the mizuhiki, "O-Rei" or "Go-Aisatsu" should be written. Beneath the mizuhiki, your name should be written.
The giving of O-rei is subject to much variation and can be very confusing, but to neglect it would be very bad form. Thus it is good to discuss it with your teacher or classmates anytime you think giving O-rei might be appropriate to decide if and what should be given.