You use the same tools that Apple uses themselves, namely XCode. All you have to do is to download additional SDKs for free from developer.apple.com
This is all that you need in theory to start developing complete high quality applications.
There are of course a whole plethora of other programs that can also be helpful, such as Photoshop/Gimp etc, 3D software, if you are into making games and so on.
There are also libraries/frameworks that will help out, such as cocos2d if you are into making 2d games etc. Some are free, and others will cost you money.
But you are right in your assumption that all you need is a mac and a developer account. XCode and sdks can be downloaded from developer.apple.com.
