I'm using WWW::Mechanize. For the methods that do not require authentication, I get those as I would any other url, and then use the perl JSON module to parse out whatever data I want:
my $response = $mech->get('http://api.stackexchange.com/1.1/questions?fromdate=' . $lasthour)
my $q = from_json($response->content())
I've used Mechanize to log into websites in the past, but the Oauth stuff is confusing, and what documentation is provided for using the API suggests that it is intended for web applications (that require registration with StackExchange?).
In particular, I am interested in the notifications method though I would expect the correct code to allow access to any of the auth-required methods.