Jerermy Kendall has written up a post for his site showing the use of his QueryAuth library for API authentication, complete with plenty of examples. The library makes it simple to sign and verify requests based on a key, secret and parameters given.
Most APIs require some sort of query authentication: a method of signing API requests with an API key and signature. The signature is usually generated using a shared secret. When you’re consuming an API, there are (hopefully) easy to follow steps to create signatures. When you’re writing your own API, you have to whip up both server-side signature validation and a client-side signature creation strategy. Query Auth endeavors to handle both of those tasks; signature creation and signature validation.
He includes code examples showing how to create a signed request, validate the signature from an incoming request and generate randomized keys and secrets. He's also created a sample implementation as a Vagrant box that sets up a Slim framework based application and uses Guzzle to make requests. He briefly looks at some of the code that makes it work and what the raw HTTP request and response look like for the result.