As far as I know, you use the Amazon mobile app to track your packages; but it only works with some of your packages. Simply launch the Amazon app on your iphone, go to orders, find what you are wanting to track, and select track package.
Understand that it won't work with all carriers. If it's being delivered by Amazon, it is usually trackable; but I've never had it work with UPS, FedEx, or USPS.
I do have an account at UPS, and can often track via their web site. I also have USPS informed delivery, which worked in my former, very rural, town, but doesn't work in my big city town.