[c#] How to use the onClick event for Hyperlink using C# code?

The onclick attribute on your anchor tag is going to call a client-side function. (This is what you would use if you wanted to call a javascript function when the link is clicked.)

What you want is a server-side control, like the LinkButton:

<asp:LinkButton ID="lnkTutorial" runat="server" Text="Tutorial" OnClick="displayTutorial_Click"/>

This has an OnClick attribute that will call the method in your code behind.

Looking further into your code, it looks like you're just trying to open a different tutorial based on access level of the user. You don't need an event handler for this at all. A far better approach would be to just set the end point of your LinkButton control in the code behind.

protected void Page_Load(object sender, EventArgs e)
{
    userinfo = (UserInfo)Session["UserInfo"];

    if (userinfo.user == "Admin")
    {
        lnkTutorial.PostBackUrl = "help/AdminTutorial.html";
    }
    else
    {
        lnkTutorial.PostBackUrl = "help/UserTutorial.html";
    }
}

Really, it would be best to check that you actually have a user first.

protected void Page_Load(object sender, EventArgs e)
{
    if (Session["UserInfo"] != null && ((UserInfo)Session["UserInfo"]).user == "Admin")
    {
        lnkTutorial.PostBackUrl = "help/AdminTutorial.html";
    }
    else
    {
        lnkTutorial.PostBackUrl = "help/UserTutorial.html";
    }
}