Create a new Xcode project from the startup window or by navigating to:
File > New > Project
An Xcode project is a folder with settings, code files, and resources. Using the Xcode app you'll be able to turn these files into an app that you can run on an iPhone, iPad, or the Mac.
Xcode is bundled with an iOS Simulator, which is a virtual iPhone on your Mac. You don't need to own an iPhone to get started, you just need a Mac.
If you want to install the app that you are creating on your iPhone, you'll need to register with Apple for the iOS Developer Program. It's $99/year + taxes and it allows you to test your app on your devices, or even send it to friends to try out.
When you first start, you don't need to register for the paid developer program. Wait until you have a working app, or are ready to submit to the App Store.
If you're in college, most universities are part of a special student/faculty program, which can allow you to test on your iPhone for free (but you can't submit to the App Store until you make a paid account).