So, here's what it looks like with a few tracking numbers entered. The app is free, however you can pay for a $1.99 per year subscription to be able to use the website, and enter an unlimited amount of tracking numbers. Without a subscription, you can only enter three.
Here's the screen where you enter it. I find that if you've already copied the number to the clipboard, it automatically shows up in the 'Number' field above. Be sure to select the right courier - it tends to default to USPS. You can also label each number, I find it handy to put the name of the online shop I got it from.
Parcel is available on the AppStore and Google Play.