Are there any good tutorials, for someone new to DirectX development? I'd like to use the SharpDX library in a project, but am completely new to this sort of graphics programming. I'm looking for a good resource for very beginner-level DirectX samples, either on the web or in print? I assume the code there will be C++, but I'm hoping they'll be straightforward enough for me to map to C#.
You might want to have a look at Microsoft XNA. It's not the whole DirectX deal but it comes close in terms of features. To understand the interface, you need (basically) no prior knowledge of DirectX/C++. It comes with its own abstractions and might thus be more approachable for you if you don't need as much low-level access as DirectX (and its managed wrappers) would normally allow. Furthermore, the XNA Game Studio should come with some samples and tutorials that make it easier to get into graphics programming.
I'm sorry I can't say for sure, though, as I've only gone the C++/DirectX route myself.
Riemers.net has some pretty easy to follow tutorials on programming wwith DirectX directly from c++ or with XNA. Helped me a lot!
Excuse the self promotion, but I'm in the process of writing some tutorials for Windows 8 Metro using SharpDX and C#, starting from the basics. You can find them in my blog.
Jose Fajardo has a collection of SharpDX demos, but since they use XAML interop, they are pretty hard to understand unless you have some knowledge of Windows 8 development.
And the full package of SharpDX comes with some nice examples, too.