If I develop an app for iPhone or iPad, how much does Apple charge me?
If you want to develop HTML5 web apps that run in Safari on your Mac/iPhone/iPad, it's free.  These apps can be designed as web clippings for your device as well.

If you want to develop Simulated iOS apps that run on the iPhone/iPad Simulator on a Mac, it's free (after the cost of your Intel Mac with Snow Leopard or Lion), or maybe $5 to download the tools from the Mac App store.

If you want to develop, install and run a native iOS app on any stock OS iPhone or iPad, you need to pay $99/annum to enroll in Apple's iOS Developer program.  

If you want to submit a native app or an app encapsulated HTML5 web app to Apple's iTunes App store, you need to be enrolled in the same $99 per year iOS Developer program.

If your app is a paid app that they approve for distribution from their App store, Apple pays you around 70% of what it charges the customers (less if there's a VAT tax).

Added: Starting with Xcode 7, and with a valid AppleID, you can use a personal profile to install apps developed using Xcode on your directly connected personal iOS devices, without paying $99 for an Apple Developer enrollment.  But apps installed this way are reported to have a short expiration date, around 1 week or so.