[DreamTheater]

function getDayOfWeek (date) {
    var dayOfWeek;

    date = date.match(/(\d{2})\.(\d{2})\.(\d{4})/);

    switch (new Date(date[3], date[2] - 1, date[1]).getDay()) {
        case 0:
            dayOfWeek = 'Воскресенье';
            break;
        case 1:
            dayOfWeek = 'Понедельник';
            break;
        case 2:
            dayOfWeek = 'Вторник';
            break;
        case 3:
            dayOfWeek = 'Среда';
            break;
        case 4:
            dayOfWeek = 'Четверг';
            break;
        case 5:
            dayOfWeek = 'Пятница';
            break;
        case 6:
            dayOfWeek = 'Суббота';
            break;
    }

    alert(dayOfWeek);
}

getDayOfWeek(prompt('Введите дату в формате dd.mm.yyyy'));