It is recommended to book tickets early, if you are planning to go Amritsar. There are premium trains like Shatabdi Express or Volvo buses are fastest way to reach Amritsar. In case you have not booked tickets early, go direct to Kashmiri Gate Bus Adda, and try to find bus either direct to Amritsar or Jalandhar. Jalandhar is 80 km before to Amritsar and there are few govt buses on Delhi Amritsar Route. You can also book tickets or buy last minute ticket for private buses, they run just nearby area like Majnu ka Tila or Kashmiri Gate.