I am working on this process myself right now, and it's a fairly complex undertaking for a full document-based application that uses a few frameworks. My Carbon app has dozens of menu items, the interface is built with Carbon Nibs and implemented using Carbon event hooks. The programming language is C++. Going back in history, the original Mac classic version was implemented in straight C, so there's a little bit of legacy from that era too. Resource-based PICS for example!
There are several approaches one can take, so it depends on your particular situation how to proceed. In my case I decided to start with a bare Cocoa document-based project and start building the document loading code, because the hooks for that are already in place in the empty project. This seems like a good place to start for me, because it gets me into the mode of working with Cocoa and thinking about the app in terms of smaller pieces.
You really have to take a methodical approach and look at what your app depends on in Carbon versus which parts of your app are independent - for instance your abstract classes. If your app is in C++ there may be some pitfalls with converting over to pure Objective-C. Operator overrides can be tricky to notice, for example.
You can mix C++ with Objective-C, as described in Apple's Carbon-Cocoa Integration Guide and around the web you can find plenty of C++ wrappers for Cocoa foundation objects like NSStrings. So if you already have C++ classes that wrap CFString, these can come in handy.
Generally-speaking, you can leave your data storage just as it is. If you use malloc() and calloc() to make a linked list of structs, there's no special reason to move over to an NSArray. You won't get better performance. The real change comes in the interfaces, the way you call and access that data from other objects. If you decide to mix C++ and Objective-C objects in the same app it helps to encapsulate as much as possible. That is, as much as possible make your abstract C++ classes only refer to their own data and that of other C++ objects. Eventually this will make it easier to transition them to Objective-C.
If you're transitioning from one event model to another or from Carbon port-based imaging to Cocoa's views-based imaging, it's probably best to start with a fresh Objective-C app and bring over your model classes first. Add some test functions to make sure they all work within the new language. If your app is anything like mine (old) then it probably needs to display some things larger, and to have more polish in the interface. This is a good time to rebuild those parts piece-by-piece.
There's definitely no great shortcut. The PDF linked above is the best document I've found on the topic.