i would advise you to call the spicejet customer care and ask exactly from where the flight will be picking up the passengers, also ask if there would be any passage from the metro to that platform..
although i think that numerous people use metro so they must be providing the shuttle service from the main hub to wherever the flight will be boarded, so i don't think that catching a flight from delhi is gonna be an issue..
plus about your train, when the train arrives to delhi, just pick the next metro available, as they run every few minutes and reach the airport asap..
in any case, after confirming from spicejet, if there is no other option, just do what akash has suggested above, take the metro and reach dhaula kuan, from there, take an auto/taxi/cab to the 1d terminal. but as the gap between you train's arrival and flight is just 2hrs (max), i'd suggest you to call a radio cab and ask him to pick you up from dhaula kuan or if money ain't an issue, simply take a cab from the station to the airport, in normal conditions, it would not take more than 1hr (% 10 minutes).