WPF is, as already described, a combination of XAML (markup) and C#/VB.NET/any other .NET language. All of it can be edited in any text editor, even Notepad included in Windows, and then compiled from the command line. However, most developers prefer to use an IDE (Integrated Development Environment), since it makes everything, from writing code to designing the interface and compiling it all so much easier.
The preferred choice for a .NET/WPF IDE is Visual Studio, which costs a lot quite a bit of money though. Luckily, Microsoft has decided to make it easy and absolutely free for everyone to get started with .NET and WPF, so they have created a free version of Visual Studio, called Visual Studio Express. This version contains less functionality than the real Visual Studio, but it has everything that you need to get started learning WPF and make real applications.
The latest version, as of writing this text, is Microsoft Visual Studio Express 2012. To create WPF applications, you should get the Windows Desktop edition, which can be downloaded for free from this website: http://www.microsoft.com/visualstudio/eng/products/visual-studio-express-for-windows-desktop.
After downloading and installing, you can use this product for 30 days without any registration. After that, you will need to register it on the above mentioned website, which is also completely free.