Here is the floor map of SHIN-CHITOSE airport.
フロアマップ | 新千歳空港ターミナルビル
Arrival gates are on 1st floor and 2nd floor. Find the blue boxes with number 1 to 5 on 1st floor and brown boxes with A to E on 2nd floor which correspond to air lines. I don't know which gates are domestic or international.
The gates to JR(on B1F) is at blue boxes 3 and 4 on the 1st floor.
This page will guide you for the reservation of tickets of JR Hokkaido.
Train Reservation ｜ Rail passes & Tickets ｜ HOKKAIDO RAILWAY COMPANY