I'm travelling from Hangzhou to Shanghai and I want to travel by train please advise.

High-speed train service between the two places are very convenient. You can easily take that at Hangzhou Railway Station to SH Hongqiao Railway Station.

Now chinese people can buy tickets online in 12306,but this website does not have English.If you can read chinese characters you can buy tickets here.and you can check the schedule here as well.
You can use your passport number to book the tickets.
Ticket is also available in the railway station windows and vendors.
The price is the same.
There are numerous trains traveling between hangzhou and SH so it will be very easy to get the ticket.