On the Web Development Blog there's a recent post about connecting your PHP application with the Flickr API to search for photos with the help of a simple class.

We will be using the php function "file_get_contents" to receive data from flickr. The data which we will receive will be a serialized PHP array which means all we need to do is unserialize the array and we will easily be able to use the data returned. As an alternative we can use a cURL function to get the data, for example if the function "file_get_contents" is not allowed on your web host.

They show how to get your API key from the Flickr website and the sample code that you'll need to make a GET request (with file_get_contents) and an example of a loop displaying the response.