cR_Andrew, a Platinum or Diamond membership allows those privileges.
Teaching Chess via Internet

As DrawMaster said, this is a premium feature, but it has everything the OP described - including the possibility of using Voice Chat within Live Chess.
http://support.chess.com/Knowledgebase/Article/View/160/13/how-do-i-use-the-live-analysis-board
Thank you for ideas.
I was already aware of the Live Analysis feature here, but I knew it required Premium membership to use, which my friend is not adverse to purchasing. (He wants to learn chess for a while before he decides if he wants to invest more time and money into it.)
After reading DeepGreene's link, I realize that a Premium membership is required to create or accept control of another's analysis board. Once I have created an analysis board, can my friend (who is not a Premium member) use it? Or is this prohibited by "accept control of another's analysis board"?
I will also visit ICC like padman suggested. Hopefully, it's what I am looking for.
Edit: It seems the lecturer tools offered at ICC require a membership to use. Free solutions are preferred. My friend is new to chess - I just taught him how the pieces move - and he would not like to pay until he is certain his interest in chess is enough that he wants to invest more time and money.
One of my friends is interested in learning chess. He asked me to teach him what I know, but it can be difficult to teach someone through words alone. (We can't meet up to play a game of chess over the board as we live in different states.)
Chess.com has a great interface for playing chess with other people, but its use as a pedagological tool is limited. I can't move the pieces for my opponents, highlight squares, take back moves, etc.
Does anyone know of a program or website that offers what I have just described? It would have to be free. It would also be nice not to have to download something, so a website is preferable.
Thank you for your ideas!