I know I'm missing a critical piece but can't figure it out. How do I get
just the name of the file they selected (without path)?

Sub CopyFilesMacro()

Application.ScreenUpdating = False

Sheets("Input").Select
MyPath = Range("B2").Value

MsgBox ("As soon as you click the OK button, a Browse Dialog box will " _
& "pop up. Use it to choose the files you want to copy to the
location shown " _
& "in cell B2 of the Input sheet.")

Dim fd As FileDialog

Set fd = Application.FileDialog(msoFileDialogFilePicker)

Dim vrtSelectedItem As Variant

With fd

If .Show = -1 Then

For Each vrtSelectedItem In .SelectedItems

FileCopy vrtSelectedItem, MyPath & "\" &
vrtSelectedItem.Name & ".xls"

Next vrtSelectedItem
Else
End If
End With

Set fd = Nothing
End Sub