Timeout error on a callout to third party REST API

Catch the CalloutException

try { 
//Execute web service call here 
HTTPResponse res = http.send(req); 

//Helpful debug messages 
System.debug(res.toString()); 
System.debug('STATUS:'+res.getStatus()); System.debug('STATUS_CODE:'+res.getStatusCode()); 
} catch(System.CalloutException e) { 
//Exception handling goes here.... retry the call, whatever 
}

Example of setting a custom timeout for HTTP callouts using the Apex HTTPRequest object

1	HttpRequest req = new HttpRequest();

2	req.setTimeout(2000); // timeout in milliseconds