You are facing two separate challenges, each of which can be addressed.
Your age: There are some things which (depending on which State or country you live in - you didn't fill in your location) you are likely to need a parent's help for. For example, you need a bank account - preferably a checking account with a debit card. You may also need one to sign up for things. You would do well to get a phone number that will get through to you without bothering the family (such as a pay-as-you-go cell phone). You may not have much trouble getting a couple of free email addresses - one specifically for business use, one for other correspondence) - but some providers require you to be "of age".
You are lucky in one regard: COPPA rules would be downright crippling if you were under 13.
Some affiliate programs and sites will not accept registrants younger than 18 (a few even go to 21). The same is true for a number of other useful resources.
Zero investment: This is really a misnomer. You can do a lot - even make a fortune - without spending significant money, but you will be "investing" a
lot of time and effort.
The first thing you need is something to promote. The easiest way is to become an affiliate for some product or site. The hardest way is to create something (eg. write a book) yourself and try to promore it. There are a lot of articles about both options here.
Another option is to get something to resell - either something in the Public Domain, or some of the thousands of products available with Resale Rights. I don't suggest this option at first, since you need to set up a web page to sell them effectively. But once you are at the point of putting up effective sales sites, they can be a
very profitable way to go.
Next, you need a way to promote it. See the threads here about social media marketing, article marketing, blogging (technically a subset of SM marketing), and so on for ways you can do that at little or no cost. You can also get some good ideas from books like (
warning: shameless plug ahead) the one you can get for
free at
http://list4wealth.comFor a little bit of money, you can do things like register, rework, and resell websites. But you need to learn what you are doing for that.
You can also offer your services online (as steveiscute mentioned), for a more conventional (but likely less profitable) way of earning money online.
There are really a lot of ways to go, to make money with little or no cash investment. You will have to overcome some hurdles (a few more than most of us), but it is eminently doable.
Jorey
.