It's all about marketing yourself. If you believe you have the skills, make them believe it too.

Whether it is an official interview position or a networking opportunity, always make sure to take advantage and sell yourself. If you contribute to open source, highlight it in your conversation. If you''ve developed any applications or even simply learned a new technology/programming language, never fail to mention those. Do not let the lack of professional experience deter you.

As a developer, I would also suggest to create a portfolio of your work, no matter how small. If this portfolio is technology-based, like a well designed website or app, that highlights your skills even more and can serve as a great first impression and good conversation starter.