Here are the time table and trains number. Note that most trains are usually arriving half an hour to one hour late in Haridwar.
On the first floor of New Delhi Station, there is a Tourist Bureau Open 24/24-7/7 with seats reserved for tourists.
It is mandatory to have your passport when booking your ticket.
You are better off booking to Haridwar, as only one train goes to Rishikesh and it is the worse because it is a passenger train.
The only luxury train is the Shatabdi (2017) for around 500 Rs. including free meal and drinks.
Trains Running Between New-Delhi and Haridwar:
Trains Running Between Old-Delhi and Haridwar: