first off teen here means someone under 18. it seems one of the best ideas for making some extra cash would be to start a website that can generate cash and or promote the service a teen can offer. However to buy domains and web hosting plans one needs a credit card that teens cannot get, or pay pall that teens cannot get because teens cannot make checking accounts. Yes there is student account for pay pal but the teen has limited control then over the account. and what about when the teen wants to leave the account so as to make one of their own? I see no way to transfer student sub account to a full account. As far as i can tell there is no way for a teen to make their own site, especially when many services require you to be 18, such as email services, affiliate programs, and all programs that could be paying the teen.
Can t your parents help you? or are you one of the Lost Boys? lol no seriously why not ask a parent or guardian to help you with the finances and then you can go ahead and start your website.
You could try a completely free home based online business.Minimum age to start is 13 years old.