NOTE: Most of this requires access to a Mac computer.
Download and Register Corona SDK
Go to http://www.anscamobile.com/corona/ and download the Corona SDK. It is fairly trivial to install onto your Mac so I will not discuss that here. If you need help with that please refer to the ansca mobile site.

Build Your App
After you have Corona up and running select one of the samples and load it into the simulator. From the Corona Simulator menu select Fild->Build->iOS. This will create a folder named after the sample ie. sampleapp.app.

Converting .app folder To iTunes Application File(.ipa)
Make a new folder and call it "Payload". Copy the complete yourapp.app folder inside of the newly created Payload folder. Click on the folder and choose "Compress". Now you should have a yourapp.zip file that you will need to rename to yourapp.ipa. Once you have your ipa file you can install it from iTunes by dragging and dropping into the Applications folder in iTunes.

If you want to show your application's artwork instead of a generic application icon you will need to place a 512x512 jpeg file called iTunesArtwork sans extension into the zip alongside the Payload folder. Do not place inside the Payload folder.

Once you have copied over the application to iTunes you will need to hook your phone up, make sure the new application is selected for syncing, and sync your phone. You should now have the sample application on your phone. Enjoy!