Это можно сделать двумя способами.
Первый способ:

Private Declare Function SendMessage Lib "user32" Alias "SendMessageA" _
(ByVal hWnd As Long, ByVal wMsg As Long, ByVal wParam As Long, _
lParam As Any) As Long
Private Declare Function ReleaseCapture Lib "user32" () As Long

Const HTCAPTION = 2
Const WM_NCLBUTTONDOWN = &HA1

Private Sub Form_MouseDown(Button As Integer, Shift As Integer, X As Single, Y As Single)
If Button = 1 Then
ReleaseCapture
SendMessage hWnd, WM_NCLBUTTONDOWN, HTCAPTION, 0&
End If
End Sub

Dim x0 As Single, y0 As Single

Private Sub Form_MouseDown(Button As Integer, Shift As Integer, X As Single, Y As Single)
x0 = X
y0 = Y
End Sub

Private Sub Form_MouseMove(Button As Integer, Shift As Integer, X As Single, Y As Single)
If Button = 1 Then
Form1.Left = Form1.Left + X - x0
Form1.Top = Form1.Top + Y - y0
End If
End Sub