Do I need to book bullet train ticket in advance or can buy it at the station before departure

I am arriving to Beijing Central Station on the 23rd of May at 11.40am. I would like to travel to Shanghai on the bullet ride as I am flying from Pudong Airport to New Zealand 24th of May at 14:15 (pm). Do I need to book ticket in advance and what is the best way to get from Central Railway Station where I arrive to South railway station from where bullet rides depart to Shanghai? Thank you.