Starting from Asansol, head towards Station Road and turn right onto Delhi-Kolkata Highway. Turn right onto NH 60 and turn left to stay on that. Then turn left towards AH 45/ NH 6 and continue straight onto OT Road. Continue onto AH 45/ NH 5 and go through 1 roundabout. Take a slight left onto Cuttack-Puri Bypass. Continue onto the Bypass road and then take a slight left onto Jagannath Sadak/NH 203. After staying slight lefts, turn left onto Jagannath Sadak and turn left onto NH 203. And you enter Puri.
Hope the directions help. To know more what to do when there, check out ixigo's
Puri travel guide page.