Overview
Objective C is THE object oriented programming language for the Mac OS X platform. You can, if u want, compile programs written in other programming languages such as C++, Ruby, Python and PHP. But that means that you're probably on your own since the official operating system development frameworks cater mainly for C, Objective C and Java. Carbon for C, Cocoa for Objective C and for Java it's the Mac OS X implementation of Java.
Objective C or Objective-C?
Here's another thing about Objective C; the official/original name is actually spelt with a dash. So it's "Objective-C" rightfully. The short form for Objective-C is Obj-C.
History
In the late 80's NeXT bought the rights of Objective-C from StepStone (the original creators) and since Apple acquired NeXT in mid 90's, Apple is now the rightful owner of the programming language and its trademark. Both NeXT and Apple are founded by Steve Jobs. [Source: http://en.wikipedia.org/wiki/Objective-C]
Language makeup
So what's Objective C really? Is it a variant of C just like C++? A Java clone? How "C" is Objective C?
Objective C borrows its object oriented methodology heavily from SmallTalk but otherwise uses C syntax. In fact, the Objective-C compiler can compile any programs written in standard C. It does OOP in a very different way from Java at the syntax level also, but all the concepts of class, object and inheritance are pretty much the same. Objective-C is sometimes described as a "thin" layer on top of C, so knowing ANSI C will help in the learning process.
Development tools
You can download the official development tool for the Mac OS X platform. Called Xcode, it's an editor, source code versioning client, debugger, project management tool and documentation reader. The standard SDK comes with instruments for profiling, interface builder and so much more.
The underlying compiler that runs in the official Apple SDK is actually the open source GCC compiler. As such, the GCC compiler itself is a 100% compatible alternative. I believe that an eclipse plugin for Objective-C is already available or is in the making.
Unofficial Objective-C CHEAT SHEET
Lastly, I would like to comment that it's not easy to learn the Objective C syntax by reading the official programming guide from Apple. A good starting point would be this [Unofficial Objective-C Cheat Sheet]