If you don't mind including Microsoft.VisualBasic.dll in your project, you can do it this way:
var audio = new Microsoft.VisualBasic.Devices.Audio();
audio.Play("some file path");
If you want to do more complex stuff, the easiest way I know of is to use the Windows Media Player API. You add the DLL and then work with it. The API is kind of clunky, but it does work; I've used it to make my own music player wrapper around Windows Media Player for personal use. Here are some helpful links to get you started:
Building a Web Site with ASP .NET 2.0 to Navigate Your Music Library
Windows Media Object Model
Let the Music Play!
EDIT:
Since I wrote this, I've found an easier way, if you don't mind including WPF classes in your code. WPF (.NET 3.0 and forward) has a MediaPlayer class that's a wrapper around Windows Media Player. This means you don't have to write your own wrapper, which is nice since, as I mentioned above, the WMP API is rather clunky and hard to use.
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