REST API key generation strategy

Question

I need to provide authorization and authentication for my REST APIs implemented using JAX-RS standard, which are meant to be consumed from mobile clients and some devices. I have multiple devices with unique device identification which can POST some data. Mobile clients are just using GET requests to display that data. I am more concerned about the POST part, where I want to authenticate the clients. Also, I would like to keep it simple. I am thinking of using a simple HTTP basic authorization over HTTPS, with an API key. My question is how do I generate this API key?