1. In Solution Explorer go to your project, right click on References then Add reference…
2. Search for Compression and select System.IO.Compression.FileSystem then press OK.
3. Add Imports System.IO.Compression to the top of your code file (before any class or module, with the other Imports statements).

Option Explicit On
Option Strict On

Imports System.IO.Compression

Public Class Foo

    ...

End Class

Plese note that this class (ZipArchive) is only available from .NET verison 4.5 onwards

System.IO.Compression.ZipFile.CreateFromDirectory("myfolder", "archive.zip")

Create archive.zip file containing files which are in myfolder. In example paths are relative to program working directory. You can specify absolute paths.

System.IO.Compression.ZipFile.ExtractToDirectory("archive.zip", "myfolder")

Extracts archive.zip to myfolder directory. In example paths are relative to program working directory. You can specify absolute paths.

' Create filestream to file
Using fileStream = New IO.FileStream("archive.zip", IO.FileMode.Create)
    ' open zip archive from stream
    Using archive = New System.IO.Compression.ZipArchive(fileStream, IO.Compression.ZipArchiveMode.Create)
        ' create file_in_archive.txt in archive
        Dim zipfile = archive.CreateEntry("file_in_archive.txt")

        ' write Hello world to file_in_archive.txt in archive
        Using sw As New IO.StreamWriter(zipfile.Open())
            sw.WriteLine("Hello world")
        End Using

    End Using
End Using