I've read the wiki articles on the subject of TF2 coaching, but none of them detail what is actually involved and what is expected of a coach. Can someone explain this in more detail please, as I feel that I might be interested.
When you sign up on the main menu, you will get an alert when someone has asked for a coach.(Usually very quickly)
If you accept, you will be automatically connected to the server they are on in a spectators type view. The chat and voice chat are both limited to the player you are coaching. Also, you have a few extra features, such as "Go Here","Attack This", or "Defend This" that you can place anywhere. There is a limit of 30 units you can travel from the student.
What's usually expected of a coach is general friendliness and patience. There's players are generally new to the game and want to learn. However, you will come upon trolls who just want to waste your time. There is no punishment for leaving a student early.
After your time with eh student is over, you will be put back into the main menu.
You can then "sign up" again and get another student to teach about the basics of the game.
My tip for coaching is to point then towards the easier classes to play, then advise them to try out different classes once they get used to the feel of the class. Make sure to tell them not to worry about deaths, it's part of the game.
Overall, just give tips, be nice, and lead the way in not being frustrated with this awesome game.