Here is some code to get you started.

Code:
//Array to hold message days
var dayMessages:Array = new Array();
dayMessages[0] = 'This is Sunday message';
dayMessages[1] = 'This is Monday message';
dayMessages[2] = 'This is Tuesday message';
dayMessages[3] = 'This is Wednesday message';
dayMessages[4] = 'This is Thursday message';
dayMessages[5] = 'This is Friday message';
dayMessages[6] = 'This is saturday message';


//Function to display message
function showDayMessage():void
{
	var d:Date = new Date();
	var tf:TextField = new TextField();
	addChild(tf);

	switch(d.getDay())
	{
		case 0:
			trace('Sunday');
			tf.text = dayMessages[0];
		break;
		
		case 1:
			trace('Monday');
			tf.text = dayMessages[1];
		break;
		
		case 2:
			trace('Tuesday');
			tf.text = dayMessages[2];
		break;
		
		case 3:
			trace('Wednesday');
			tf.text = dayMessages[3];
		break;
		
		case 4:
			trace('Thursday');
			tf.text = dayMessages[4];
		break;
		
		case 5:
			trace('Friday');
			tf.text = dayMessages[5];
		break;
		
		case 6:
			trace('Saturday');
			tf.text = dayMessages[6];
		break;
	}
}


showDayMessage();