How to create a Tooltip anywhere on the screen?

Question

Why does it matter whether it is Windows Forms, ASP .NET, etc? Because it probably affects your choices.

If it is a Windows Forms application you could create your own class that inherits from Windows.Forms.Form, set some properties and then use that.

public class MyTooltip : Form
{
    public int Duration { get; set; }

    public MyTooltip(int x, int y, int width, int height, string message, int duration)
    {
        this.FormBorderStyle = FormBorderStyle.None;
        this.ShowInTaskbar = false;
        this.Width = width;
        this.Height = height;
        this.Duration = duration;
        this.Location = new Point(x, y);
        this.StartPosition = FormStartPosition.Manual;
        this.BackColor = Color.LightYellow;

        Label label = new Label();
        label.Text = message;
        label.TextAlign = System.Drawing.ContentAlignment.MiddleLeft;
        label.Dock = DockStyle.Fill;

        this.Padding = new Padding(5);
        this.Controls.Add(label);
    }

    protected override void OnShown(System.EventArgs e)
    {
        base.OnShown(e);

        TaskScheduler ui = TaskScheduler.FromCurrentSynchronizationContext();

        Task.Factory.StartNew(() => CloseAfter(this.Duration, ui));
    }

    private void CloseAfter(int duration, TaskScheduler ui)
    {
        Thread.Sleep(duration * 1000);

        Form form = this;

        Task.Factory.StartNew(
            () => form.Close(),
            CancellationToken.None,
            TaskCreationOptions.None,
            ui);
    }
}

You can use it like this:

    private void showButton_Click(object sender, EventArgs e)
    {
        var tooltip = new MyTooltip(
            (int)this.xBox.Value,
            (int)this.yBox.Value,
            50,
            50,
            "This is my custom tooltip message.",
            (int)durationBox.Value);

        tooltip.Show();
    }

Instead of closing you could reduce the form's opacity until it disappears then close it for a nicer effect, assuming you want a duration at all.

You could also play around with the transparency colour and use a background image, etc to have shaped tooltips.

EDIT:

Here is a quick demonstration of how the CloseAfter method could fade out the tooltip form.

private void CloseAfter(int duration, TaskScheduler ui)
{
    Thread.Sleep(duration * 1000);

    Form form = this;

    for (double i = 0.95; i > 0; i -= 0.05)
    {
        Task.Factory.StartNew(
            () => form.Opacity = i,
            CancellationToken.None,
            TaskCreationOptions.None,
            ui);

        Thread.Sleep(50);
    }

    Task.Factory.StartNew(
        () => form.Close(),
        CancellationToken.None,
        TaskCreationOptions.None,
        ui);
}