There are many free classifieds where you can find people looking for a website. e.g craigslist. Have in mind though that the competition there is tough, so you should really make a good proposal to win a client.
I think it doesn't matter what is your age as long as you provide quality work. But yes, maybe you should find someone who would just work with you, speak with clients, etc, this will also let you 'learn' how to behave with clients, set terms and expectations..
I believe you can start doing small pieces of work like logos, banners, etc just to learn how to behave with clients and find out how to make them happy. Once they are happy with you - the age will hardly matter :)
