While I recommend that you try to learn recursion, actually it's not needed here. The GetFiles method in the IO namespace will let you find all files in a given directory AND it's subdirectories.
Something like this:
Imports System.IO
Dim dir As New DirectoryInfo("C:\")
For Each foundFile As FileInfo In dir.GetFiles("*.*", SearchOption.AllDirectories)
Next foundFile
In this case, the AllDirectories flag specifies that it should loop through all subdirectories recursively...