How can I tell if sheet a exists in a workbook?

I'd make a separate function for it:

Function SheetExists(SheetName As String)
    On Error GoTo no:
    WorksheetName = Worksheets(SheetName).Name
    SheetExists = True
    Exit Function
no:
    SheetExists = False
End Function

Then you can easily call it where needed, even in a formula if you wanted:

Sub ABC()
    If SheetExists("Test") Then
        MsgBox "Yay!"
    Else
        MsgBox "Boo!"
    End If
End Sub

or

=If(SheetExists("Test"),"Yay!","Boo")

Something like:

Sub DoesSheetExist()
    Dim s As Worksheet

    For Each s In Sheets
        If s.Name = "a" Then
            MsgBox "Sheet a exists"
            Exit Sub
        End If
    Next s
    MsgBox "Sheet a does not exist"
End Sub

You can check for the error. eg:

Dim A As String
    On Error Resume Next
        A = Worksheets("a").Name
        Select Case Err.Number
            Case 9
                MsgBox "Sheet ""a"" does not exist"
            Case 0
                MsgBox "Sheet ""a"" exists"
            Case Else
                Stop
        End Select
    On Error GoTo 0