Promote products that are related to teens (gadgets, cell phones, make up stuff etc...). Once you build enough popularity, the sales will come, but I suppose it will take a lot of time, since the market is kind of saturated...
Naah it's a get-rich-quick scheme. There much better money earning opportunities around. Especially if you are not a teen...
I am a teen so I had this idea. Seems like many people are for it. When I googled teen forum there was nothing that good. There was a Christian teen forum which looked best among the top 10 search results.
Developing a teen forum is the best way to earn money. Why? Well because it is the youth which firstly surfs the net. You have to find interesting topics for it.
Why are you focusing on teens? It would make more sense to pick a niche (maybe within the teen sector) and focus on that to get the initial traffic. Teenagers is such a wide market, it would be hard to compete.