You can buy your ticket at any point you like, and the sooner the better in terms of getting a lower price. Then when you get to the station, present the coupon along with either the ticket (if you have it already) or your printed reservation confirmation. If you're within the one hour window and space is still available, the agent will issue you a ticket good for the upgraded seat. Note: You cannot do this onboard the train, it must be done in the station. The conductor cannot take the coupon from you.

Just as an aside, Select Plus members get coupons that allow them to call up to two days before departure to get their upgrade.