From New Delhi, take New-Delhi Bhatinda Inter City Express to Ambala, and take bus/taxi to reach Patiala.
Check out the trains to Patiala.
Patiala is about 250 kms from Delhi, a drive around 5 hours. You can drive to Patiala from Chandigarh, via Zirakpur (on NH 7).
From Patiala, the nearest International Airport is at Delhi. The nearest domestic airport is at Chandigarh, which is around 70km from Patiala. The flight's schedule may be checked online.