It depends on what you want to do with it, but here's probably the easiest way.
On your ASP page, you would have a parent container that you wish to add your DIV to, such as:
<div id="divContainer" runat="server">
</div>
Make sure you have the 'runat="server"' element tag added to this element, otherwise your code behind will not be able to see it.
And then in your code behind:
divContainer.InnerHtml = "<div style=\"color:#ff0000;\">some new content goes here</div>";
Or for more control over the element once created, use:
System.Web.UI.HtmlControls.HtmlGenericControl divContent = new System.Web.UI.HtmlControls.HtmlGenericControl("DIV");
divContent.ID = "divContent";
divContent.Style.Add(HtmlTextWriterStyle.Color, "Red");
divContent.InnerHtml = "some new content goes here";
divContainer.Controls.Add(divContent);