You may want to check
this[
^] out. It's a compression library which supports not only zip, but other compression methods as well. Although the library is written in C#, you can use it in your VB.NET code. If you download the source codes you'll get some samples as well.
You can use the standard Windows compression as well, but I found it hard to compress multiple files into one zip archive so I recommend using the C# Zip library.
Good luck,
Eduard