You are looking for this, then:
File.WriteAllText(@"c:\some\path\json.txt",json);
And note that it will save the file using UTF8-encoding without a Byte Order Mark. If you need the BOM, you need to use the File.WriteAllText(path, content, Enconding);
Update - adding sample with SaveFileDialog:
if(!string.IsNullOrEmpty(saveFileDialog.FileName))
{
//saveFileDialog.FileName should contain the full path
//according to the documentation: http://msdn.microsoft.com/en-us/library/system.windows.forms.filedialog.filename.aspx
File.WriteAllText(saveFileDialog.FileName,json);
}