Google does not have a speech recognition API for desktops. They only have a speech recognition API for Android developers. However, you can download Microsoft's speech recognition API here: http://msdn.microsoft.com/en-us/library/ms723627(v=vs.85).aspx and you can read how to get it to work in C# here: http://windowscoding.com/blogs/blake/archive/2006/11/01/How-to-use-Microsofts-Speech-API-in-a-managed-application.aspx
Once you run the recognition api on the sample of text you want to recognize, you can simply call google.com with the "q" parameter to do a query search
Note too that Microsoft is not the only company with a speech recognition API. You are free to use any you want.