I am trying to use an authorization header in order to use the vimeo API.
It tells me to do this \'Authorization: basic \' + base64(client_id + \':\' + client_secret
Vimeo highly recommends you do not write these authentication systems yourself, but use the official libraries: https://github.com/vimeo/vimeo.php.
If you are looking for a custom PHP integration, it varies based on the way you make HTTP requests. guzzle and curl are both http request libraries, with their own ways of setting headers (http://guzzle.readthedocs.org/en/latest/request-options.html#headers and PHP cURL custom headers)
As for base64 encoding your tokens, use the method base64_encode
(http://php.net/manual/en/function.base64-encode.php)