You can buy tickets on online portals such as ctrip.com but you need to go to the ticket counter at the station with your ID to pick up the physical tickets, so reserve time
Ticket machines at station are only for Chinese IDs, you should go straight to the counter
***There are different counters for different functions, such as ticketing, ticket changes, priority windows, etc. Not all of them have english signs so make sure you ask someone in line to know which line you are lining up for because if you end up at the wrong line, you'd have to line up again
Always get your tickets early (either online or offline) especially during weekends, Jul&Aug, around Oct 1 (National Day) and Chinese new year periods (Jan-Feb but changes yearly with the lunar calendar) and other major Chinese holidays