The correct OAuth Authorization header is determined from the request params
and then set in the $request['header']['Authorization'] param of the request
array before passing it back to HttpSocket::request() to send the request and
parse the response.
So to trigger OAuth, add $request['auth']['method'] = 'OAuth' to your
request. In addition, you'll need to add your consumer key in the
$request['auth']['oauth_consumer_key'] and your consumer secret in the
$request['auth']['oauth_consumer_secret'] param. These are given to you by
the OAuth provider. And once you have them, $request['auth']['oauth_token']
and $request['auth']['oauth_token_secret'] params. Your OAuth provider may
require you to send additional params too. Include them in the
$request['auth'] array and they'll be passed on in the Authorization header
and considered when signing the request.