You can use the standard tooltip which is enabled by default (ShowToolTip = true) or enable an event bubble (an extended tooltip).

The default tooltip text is set to the event text and you can customize it in BeforeEventRender event handler.

JavaScript

<div id="dp"></div>
<script type="text/javascript">
  var dp = new DayPilot.Month("dp");
  dp.events.list = [
    {
      start: "2013-03-25T00:00:00",
      end: "2013-03-25T12:00:00",
      id: "123",
      text: "Event",
      toolTip: "my tooltip"
    }
  ]
  // ...
  dp.init();
</script>

ASP.NET WebForms

 
protected void DayPilotMonth1_BeforeEventRender(object sender, BeforeEventRenderEventArgs e)
{
  e.ToolTip = "my tooltip";
}

ASP.NET MVC

 
protected override void OnBeforeEventRender(BeforeEventRenderArgs e)
{
  e.ToolTip = "my tooltip";
}