You will need Mac OS X, you could search for tutorials on how to install OS X on a virtual machine.
Once you have access to OS X, you will need to register as an iOS developer. Registering is free and you will have access to Xcode 3 + iOS SDK (includes iOS simulator). If you need your application on an iOS device (other than the iOS simulator), you will need to purchase the iOS developer program which costs $99. Xcode 4 has now been released, but this requires purchasing if you haven't brought a developer program for $4.99. Registering as a developer also gives you access to iOS, Mac and Safari Dev Center Resources, which you will find useful at some point. You can register here for free. I recommend trying out iOS development first before purchasing, as it's hard for some people to get the hang of.
After downloading and installing Xcode 3 + iOS SDK, you may be a little lost. Answering with a step by step tutorial for your fist iOS application is a little hard, so I will provide links to resources which are very useful. Here is a very good tutorial which will help you install Xcode and write you first application. It also teaches you about the programming language you'll be using, Objective-C. Objective-C is similar to C/C++.
You may find it easier watching a tutorial instead, therefore I recommend searching for videos.
Hope this helps!