If you're using .Net 2.0, you can use the GZip or Deflate streams.
See http://msdn2.microsoft.com/en-gb/library/system.io.compression.gzipstream.aspx for an example or lookup GZipStream class in your help.
If you have .Net 1.x, you'll need some help. I liked to use SharpZipLib at http://www.icsharpcode.net/
Did you take a look at sharpziplib I believe it has the ability to zip a directory.