Corona SDK is a commercial software product from Corona Labs. It's free to use to make games for yourself but requires a paid yearly subscription to put applications in the Apple App Store or Google Play Store.
The complete documentation as well as many tutorials and guides for Corona SDK is available at http://docs.coronalabs.com.
Help with Corona applications can come from StackOverflow questions tagged with "corona": http://stackoverflow.com/questions/tagged/corona or from the official Corona forums: http://forums.coronalabs.com/. Neither Corona's forums nor StackOverflow are moderated by Coder Dojo so make sure you get permission before creating accounts and participating in discussions yourself. In the future we may have a Coder Dojo discussion forum that is moderated by us. Stay in touch with http://www.coderdojosv.com/ for the latest updates.
The introduction to Lua from this course is a good start for using the Lua programming language with Corona.
The complete Lua reference manual is available from http://www.lua.org/manual/5.2/ but it can be a bit daunting at times. Earlier editions of the book are free. The most recent free book is always available online at http://www.lua.org/pil/contents.html.
You can also check the Lua tag on StackOverflow.
When programming specifically for Apple devices, you can still use Corona SDK and continue writing in Lua. However, you might want the power of using Apple's native tools and the Objective C programming language. Apple's developer program is the only way to access documentation and tools required to build iOS programs and applications. If you just want to dip your toes in the pool and try Objective C, Code School has a Try Objective-C and Try iOS courses available. Try iOS costs money but the author of this document is a regular student of Code School courses and recommends them highly.
If you can remember all the way back to the first session, we set up provisioning profiles and certificates when building for iOS. To do this yourself requires an Apple Developer account which costs $100 per year. You can continue using the profile we created to build applications but it is limited to devices you added to the provisioning profile during that night. If you have any trouble or questions with the iOS build requirements contact Coder Dojo SV HQ.
You can, of course, continue using the Corona SDK to create Android programs and games. The Android development tools are freely available from Google and might be interesting to you. You can get them from https://developer.android.com/index.html. The Android Developer's Guide might also be interesting to you.
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