You can Upgrade your Products by spending Replicate Cards and Influence Points. When you have collected the required resources a little yellow exclamation point appears on your Products button to alert you. Tap on the button to access the Products screen.
Just like the Main Game screen the individual Product Cards will have little yellow exclamation points indicating you can Upgrade them. Tap on the Product you wish to Upgrade.
In the individual Products Card's menu you will see how much the upgrade will cost you, simply tap the green Go button to complete the upgrade.
If you happen to be lacking the necessary amount of Replicate Cards you can buy the missing cards in exchange for Super Cash.