I'm a week ahead of you on that Alaskan Cruise.
Our more seasoned fellow cruisemates will indeed offer their help (I hope).
From what I understand, an On Board Credit of some sort is the discount. ? And if this is your first cruise, I'm pretty sure your Circle privileges will also play a role in discounts.
The lines website might also be helpful in determining your Circle status and 'bonuses', which are calculated on the number of your Princess cruises previously sailed.