The usual answer to all programming questions: "It depends".
You *could* do it right on your .aspx page.
Right in the middle of the HTML and the ASP.NET tags, you could simply do
<%= System.DateTime.Today.ToLongDateString()%>
And it will be just dumped, as text, right out into your page.
But if you want it to appear in a box or a label or or or...well, "It depends." Yes, you could do it in code behind by doing something like
myDateTimeLabel.Text = System.DateTime.Today.ToLongDateString();
but I'm reluctant to say more without knowing your specifics.
I'm afraid you're going to have to begin to learn *some* of the fundamentals of programming. ASP.NET was never designed to be a 100% "drag and drop" environment. Visual Studio helps you out a lot, but it won't (and can't) do everything for you.
If you aren't working your way through some of the tutorials at
http://msdn.microsoft.com/Express already, it's time to start doing so.