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Count of weekdays:
A1 Start date
A2 End date
A3 Weekday to count between A1 and A2 (1=Sunday)
Formula: =INT((A2-MOD(A2-A3,7)-A1+7)/7)
Alternative Formula (by Daniel M.): =INT((A2-WEEKDAY(A2+1-A3)-A1+8)/7)

Last Friday of a month:
A1 Any day within given month
Formula: =DATE(YEAR(A1),MONTH(A1)+1,0)-MOD(DATE(YEAR(A1),MONTH(A1)+1,0)+1,7)
[if A1 holds last day of a month then the formula simply is =A1-MOD(A1+1,7)]
For a general solution to determine the first or the last weekday (actually, any) of a month, see here, please.

Determine whether a date is a weekend day (Saturday or Sunday):
A1 Date
Formula: =MOD(A1,7)<2

Count of working days (Mondays through Fridays without any holidays):
A1 Start date
A2 End date
Formula: =(A2-WEEKDAY(A2,2)+WEEKDAY(A1,2)-A1)/7*5-MIN(5, WEEKDAY(A1,2))+MIN(5,WEEKDAY(A2,2))
This formula is different from Excel's built-in function NETWORKDAYS (analysis add-in). It counts from A1 24:00 until A2 24:00. If you look for a NETWORKDAYS-equivalent solution, take A2 minus A1 plus 1 and subtract the count of Saturdays and Sundays (see count of weekdays above).

An equivalent solution in Excel VBA is the function cwd() shown below:

Function cwd(d1 As Date, d2 As Date) As Long
'Counts working days from d1 24:00 until d2 24:00 without holidays
'Different from Excel's networkdays()!
'Reverse("moc.LiborPlus.www") V0.2 PB 25-Aug-2009
cwd = (d2 - Weekday(d2, 2) + Weekday(d1, 2) - d1) / 7 * 5 - min(5, _
        Weekday(d1, 2)) + min(5, Weekday(d2, 2))
End Function

Function min(v1 As Variant, v2 As Variant) As Variant
min = v1: If v2 < v1 Then min = v2
End Function

Function CWPeriods(dBase As Date, rStartEnd As Range) As Variant
'Counts working days between alternating start dates and end dates in rStartEnd.
'If a start date is given but no corresponding end date then count until dBase.
'In general: start dates are counting, end dates not!
'Reverse("moc.LiborPlus.www") V0.2 PB 25-Aug-2009
Dim lc As Long
Dim i As Long, j As Long
Dim bIsStart As Boolean, bEndSeen As Boolean
Dim dStart As Date, dEnd As Date

If rStartEnd.Cells.Count Mod 2 <> 0 Then
    CWPeriods = "Range with start dates and end dates has to have even number of cells!"
    Exit Function
End If

bIsStart = True     'First cell in rStartEnd is a start date
bEndSeen = True     'We do not want to count anything if rStartEnd is empty.
lc = 0              'Initialize day count to zero

For i = 1 To rStartEnd.Rows.Count
    For j = 1 To rStartEnd.Columns.Count
        If Not IsEmpty(rStartEnd.Cells(i, j)) Then
            If bIsStart Then
                dStart = rStartEnd.Cells(i, j) - 1
                bEndSeen = False
            Else
                dEnd = rStartEnd.Cells(i, j) - 1
                If dEnd < dStart Then
                    CWPeriods = "Error! End date " & Format(dEnd + 1, "yyyy-mm-dd") & _
                        " is before start date " & Format(dStart + 1, "yyyy-mm-dd") & "."
                    Exit Function
                End If
                lc = lc + cwd(dStart, dEnd)
                bEndSeen = True
            End If
        End If
        bIsStart = Not bIsStart 'Toggle between start and end date treatment
    Next j
Next i

If Not bEndSeen Then
    lc = lc + cwd(dStart, dBase - 1)
End If

CWPeriods = lc

End Function