I understand that the price you get for transporting cargo goes lower every day, but when does this deduction start? Does it start when the industry delivers the goods to the station or when the train picks it up?
The amount you get paid is depend on the type of good, the amount of time it spends in transit (not time spent waiting to be delivered*) and the distance delivered. The formula for the penalty, taken from the wiki, is:
The Early Delivery Time, Late Delivery Time and Initial Cargo Payment can be found at the Wiki. Initial Cargo Payment is subjected to inflation.
You can also find a (less detailed, but more easy to understand) graph inside your game by going to Graphs > Cargo Payment Rates. It looks something like this:
As you can see, this matches the Wiki's formula, where certain goods have flat payment rates for certain period of time before the penalty kicks in, and after a certain point the line becomes steeper as the second late penalty kicks in.
* The amount of good waiting to be delivered at a station affects the station ratings, which in turn affects what fraction of goods the industries served by that station will give to the station to deliver.