The DotNetZip library is very well documented and easy to use.
You can download the library (just one file) from here.
This example is all that you need to write
using (ZipFile zip = new ZipFile())
{
zip.AddDirectory(@"MyDocuments\ProjectX", "ProjectX");
zip.Comment = "This zip was created at " + System.DateTime.Now.ToString("G") ;
zip.Save(zipFileToCreate);
}