I am confused about the starting elo rating of new members at chess.com. Most of them start at 1200 but some of them have 800, 1000, 1400, 1600 or even 1800. How is it decided what is the initial value of the elo rating of a new member?
You can select your starting rating on the register page by changing the skill level options.
For example, if you select "expert" your starting ratings will be 1800 (at least when I tried it).
So, to answer your question, "How is it decided what is the initial value of the elo rating of a new member?", it is decided by what option the user chooses.
Summary of the glicko system:
You have a score, like you start at 1200, but you also have a RD (rating deviation). When you first play games, you have a large RD, meaning your actual skill could be 1200 + or - a large number, but it can't tell what that skill is until you play a lot of games, decreasing your RD. Hope this helps.
Look at this link: http://www.chess.com/article/view/chess-ratings---how-they-work
It talks about the Glicko System. Ctr + F then search to find it or scroll down. Shouldn't be hard to find.