"it's NOT at ALL like VB 6.0."
You've got that right. VB has gone through puberty...
"It's really ridiculously over-complicated."
More complicated than VB6? yes. Over-complicated? No. Just like most things in computers, power and flexibility comes with the price of usability.
VB.NET is really a different animal completely than VB6 - it has much more in common with C# than it does with previous versions of VB. The good news is that VB6 has grown up, and if you're willing to spend some time to learn the .NET framework, you'll be using a top-notch language, and no longer vulnerable to taunts by Java and C# programmers.
Anyway, to answer your question...I don't know how simple this was in VB6, but it's still pretty simple in VB.NET 2005:
'assuming you already have the source
'filename in a variable named sourceFilename
Dim fs as SaveFileDialog = New SaveFileDialog()
fs.ShowDialog()
Dim destFilename as String = fs.Filename
System.IO.File.Copy(sourceFilename, destFilename)
Good luck,
-SN