First set of calculations:
Option Explicit
Dim mtd(12) As Integer
Dim DoW(7) As String


Private Sub Command1_Click()
Rem This only works for the the twentieth century
Rem In fact it doesn't work for the earliest part of the
Rem century either

    Dim yy As Integer, mm As Integer, dd As Integer
    Dim Days As Integer, numdow As Integer
    ' input 02/25/98 is Wednesday
    yy = Val(Right(txtDate.Text, 2))
    ' yy = 98
    mm = Left(txtDate.Text, 2)
    'mm = 02
    dd = Mid(txtDate.Text, 4, 2)
    'dd = 25
    Days = 365 * (99 - yy)
    ' Days = 365 * (99-98) = 365 * 1 = 365
    Days = Days + (365 - (mtd(mm) + dd))
    ' Days = 365 + (365 - (mtd(2) + 25) = 365 + (365 - (31 + 25)
    ' = 365 + 365 - 56 = 365 + 309 = 674
    Days = Days + (99 - yy) \ 4
    ' Days = 365 + (99 - 98) \ 4 = 365 + 1\4 = 365 + 0
    If yy Mod 4 = 0 And _
      mm < 3 Then
    ' yy mod 4 = 98 / 4 = 24 remainder 2
        Days = Days + 1
    End If
    numdow = Days Mod 7
    ' 674 divided by 7 = 96 with a remainder 2
    lblDOW.Caption = DoW(numdow)
    'DoW(2) = Wednesday
    
    
End Sub

Private Sub Form_Load()
    mtd(1) = 0
    mtd(2) = 31
    mtd(3) = 59
    mtd(4) = 90
    mtd(5) = 120
    mtd(6) = 151
    mtd(7) = 181
    mtd(8) = 212
    mtd(9) = 243
    mtd(10) = 273
    mtd(11) = 304
    mtd(12) = 334
    'Friday is the last day of 1999
    DoW(0) = "Friday"
    DoW(1) = "Thursday"
    DoW(2) = "Wednesday"
    DoW(3) = "Tuesday"
    DoW(4) = "Monday"
    DoW(5) = "Sunday"
    DoW(6) = "Saturday"
    
End Sub

Second set of calculations:
Option Explicit
Dim mtd(12) As Integer
Dim DoW(7) As String


Private Sub Command1_Click()
Rem This only works for the the twentieth century
Rem In fact it doesn't work for the earliest part of the
Rem century either

    Dim yy As Integer, mm As Integer, dd As Integer
    Dim Days As Integer, numdow As Integer
    ' input 10/14/88 is on Friday
    yy = Val(Right(txtDate.Text, 2))
    ' yy = 88
    mm = Left(txtDate.Text, 2)
    'mm = 10
    dd = Mid(txtDate.Text, 4, 2)
    'dd = 14
    Days = 365 * (99 - yy)
    ' Days = 365 * (99-88) = 365 * 11 = 4015
    Days = Days + (365 - (mtd(mm) + dd))
    ' Days = 4015 + (365 - (mtd(10) + 14) = 4015 + (365 - (273 + 14)
    ' = 4015 + 365 - 287 = 4015 + 78 = 4093
    Days = Days + (99 - yy) \ 4
    ' Days = 4093 + (99 - 88) \ 4 = 4093 + 11\4 = 4093 + 2 = 4095
    If yy Mod 4 = 0 And _
      mm < 3 Then
    ' 88 mod 4 = 88 / 4 = 22 remainder 0 by mm not < 3
        Days = Days + 1
    End If
    numdow = Days Mod 7
    ' 4095 divided by 7 =  585 with a remainder of 0
    lblDOW.Caption = DoW(numdow)
    'DoW(0) = Friday
    
    
End Sub

Private Sub Form_Load()
    mtd(1) = 0
    mtd(2) = 31
    mtd(3) = 59
    mtd(4) = 90
    mtd(5) = 120
    mtd(6) = 151
    mtd(7) = 181
    mtd(8) = 212
    mtd(9) = 243
    mtd(10) = 273
    mtd(11) = 304
    mtd(12) = 334
    'Friday is the last day of 1999
    DoW(0) = "Friday"
    DoW(1) = "Thursday"
    DoW(2) = "Wednesday"
    DoW(3) = "Tuesday"
    DoW(4) = "Monday"
    DoW(5) = "Sunday"
    DoW(6) = "Saturday"
    
End Sub

Third set of calculations:
Option Explicit
Dim mtd(12) As Integer
Dim DoW(7) As String


Private Sub Command1_Click()
Rem This only works for the the twentieth century
Rem In fact it doesn't work for the earliest part of the
Rem century either

    Dim yy As Integer, mm As Integer, dd As Integer
    Dim Days As Integer, numdow As Integer
    ' input 02/12/80 is Tuesday
    yy = Val(Right(txtDate.Text, 2))
    ' yy = 80
    mm = Left(txtDate.Text, 2)
    'mm = 02
    dd = Mid(txtDate.Text, 4, 2)
    'dd = 12
    Days = 365 * (99 - yy)
    ' Days = 365 * (99-80) = 365 * 19 = 6935
    Days = Days + (365 - (mtd(mm) + dd))
    ' Days = 6935 + (365 - (mtd(2) + 12) = 6935 + (365 - (31 + 12)
    ' = 6935 + 365 - 43 = 6935 + 322 = 7257
    Days = Days + (99 - yy) \ 4
    ' Days = 7257 + (99 - 80) \ 4 = 7257 + 19\4 = 7257 + 4 = 7261
    If yy Mod 4 = 0 And _
      mm < 3 Then
    ' yy mod 4 = 80 / 4 = 20 remainder 0 and mm is less than 3
        Days = Days + 1
    ' 7261 + 1 = 7262
    End If
    numdow = Days Mod 7
    ' 7262 divided by 7 has a remainder of 3
    lblDOW.Caption = DoW(numdow)
    'DoW(3) = Tuesday
    
    
End Sub

Private Sub Form_Load()
    mtd(1) = 0
    mtd(2) = 31
    mtd(3) = 59
    mtd(4) = 90
    mtd(5) = 120
    mtd(6) = 151
    mtd(7) = 181
    mtd(8) = 212
    mtd(9) = 243
    mtd(10) = 273
    mtd(11) = 304
    mtd(12) = 334
    'Friday is the last day of 1999
    DoW(0) = "Friday"
    DoW(1) = "Thursday"
    DoW(2) = "Wednesday"
    DoW(3) = "Tuesday"
    DoW(4) = "Monday"
    DoW(5) = "Sunday"
    DoW(6) = "Saturday"
    
End Sub