How can a 19-year-old find web programming work?
lothia: Develop your own website which will be your portfolio to show everyone. 
Generally not having a degree will hurt you a lot and will generally lower the amount you can require for developing a website. There are websites such as 99designs.com which you can offer your designs to people that post how much money they are offering. This can help get your designs and name out there. 
The best bet IMO is to go to Uni next year and during your first few years build that portfolio, if you are going to a mid to large school you can sometimes get grants from certain schools if you offer to develop a website for them (I know someone who got half of his masters degree paid doing this). 
However in todays world the degree really does help.