Use SQL code instead of program loops
For example, the code:
        Do While Not tblPersons.EOF
            If tblPersons("Name") = looking Then
                MsgBox "Your number is " & tblPersons("Number")
            End If
            tblPersons.MoveNext
        Loop
could be replaces with:
        Set qryPersons = dbsDb.OpenQuery("SELECT Number from Persons Where Name ='" & looking & "'")
        Set rstPersons = qryPersons.OpenRecordset
        If Not rstTables.EOF
            MsgBox "Your number is " & rstPersons("Number")
        End If