Flying into Manchester and then taking the train to Penrith in the Lake District. Is the train station in the airport or do we have to leave the airport?
There is a "Skylink" moving walkway that connects Terminal 1, train station, and Terminal 2.
Most airports are pretty good at posting information on their websites, making them the first place to look for information.
http://www.manchesterairport.co.uk/to-and-from-the-airport/train/