How do I test my iOS Apps

Update: Added section 'Automated testing for iOS4'

As a professional tester my suggestion is that you should have a healthy mix of automated and manual testing. The Examples below are in .net but it should be easy to find a tool for whatever technique you are using.

AUTOMATED TESTING

• Unit Testing
  Use NUnit to test your classes, functions and interaction between them.
  http://www.nunit.org/index.php

• Automated Functional Testing
  If it's possible you should automate a lot of the functional testing. Some frame works have functional testing built into them. Otherwise you have to use a tool for it. If you are developing web sites/applications you might want to look at Selenium.
  http://www.peterkrantz.com/2005/selenium-for-aspnet/

• Continuous Integration
  Use CI to make sure all your automated tests run every time someone in your team makes a commit to the project.
  http://martinfowler.com/articles/continuousIntegration.html

• Automated testing for iOS4
  Automate the testing of your application by scripting touch events using the new UIAutomation Instrument.
  Some links:
  

  • http://answers.oreilly.com/topic/1646-how-to-use-uiautomation-to-create-iphone-ui-tests/
    
  • http://cocoawithlove.com/2008/11/automated-user-interface-testing-on.html
    
  • http://alexvollmer.com/posts/2010/07/03/working-with-uiautomation/
    

MANUAL TESTING
As much as I love automated testing it is, IMHO, not a substitute for manual testing. The main reason being that an automated can only do what it is told and only verify what it has been informed to view as pass/fail. A human can use it's intelligence to find faults and raise questions that appear while testing something else.

• Exploratory Testing
  ET is a very low cost and effective way to find defects in a project. It take advantage of the intelligence of a human being and a teaches the testers/developers more about the project than any other testing technique i know of. Doing an ET session aimed at every feature deployed in the test environment is not only an effective way to find problems fast, but also a good way to learn and fun!
  http://www.satisfice.com/articles/et-article.pdf

Take a look at automated testing tools. Supports automated and manual testing/sending feedback from within the app with annotated screen shots

I suggest you take a look at the iPhoneUnitTests sample code posted by Apple on their developer site.