The nearest railhead/airport is Jammu. To travel to Katra from here, you can take cabs Rs. 820 for an Indica, Rs. 890 for an Ikon, or buses from the bus stand just outside the railway station.
If traveling from Delhi, there are options to travel in Buses which go direct to Katra, but the train journey is more comfortable.
You can travel direct to katra by train. You can catch Shri Shakti express, NDLS-SVDK Premium from Delhi.