Pack some nice homemade food, cause this isn't a short trip !
There are direct trains but no direct flights for this journey. kolkata (West Bengal) to Rishikesh (Uttarakhand) distance is 1523 km and you can get there by flight + cab in just over 9 hours and 33 minutes or by train fares starting from ₹ 510.
It's pleasant weather in daytimes, but can get really cold at nights.