BY FLIGHT: First you choose flights there is only one flights come to Srinagar i.e. Air India . This flights is not direct they take 1 stop in delhi and operate next day from New delhi to Srinagar take 27 hours minimum to reach.
BY TRAIN : There is also option to come by train. There is only one train operate from Surat that is Swaraj Express. Swaraj Express operates four days in a week i.e. Monday, Tuesday, Friday, Saturday .but train drops you at Jammu Tawi Railway the distance is 1480 kms & take approx 27 hours to reach Jammu and than you choose taxi for further journey.
BY ROAD : There is no bus service or operator from Surat to Jammu Kashmir. You take bus from Surat to Delhi ISBT & than take another Bus from ISBT Kashmiri Gate Delhi to Jammu Bus stand the approx distance is 600 kms & it will take 11 hours approx to reach Jammu by road. In Jammu there are various option to reach Kashmir you take local sharing Cabs local bus service and individual cabs . Bus service operates in the night only you take Volvo buses as well as local buses from Jammu Bus stand & rest services like individual taxi & sharing cabs you take from exit point of Railway station , Jammu Bus stand & Gumat chowk they operates whole day. The distance between Jammu to Kashmir is approx 300 Kms & it will take 8 to 10 hours to reach Kashmir.