How do I Keep a user logged in for 2 weeks?

Add a hash key or a random string to both the cookie and the database (both the same key). If the cookie and database value are the same, when the user starts a new session, sign him/her in again. When the user reaches the two weeks, remove the secret key from the database using a cronjob (Unix) or scheduled task (Windows).

Warning: Do not rely on the cookie expire date, since people can hack their browser.
Rule: NEVER, EVER trust ANY of your users!

You can set the global session timeout (the value is in minutes) in web.config eg.

<system.web>
    <authentication mode="Forms">
          <forms timeout="20160"/>
    </authentication>
</system.web>

This will be for all authenticated users. If you want to use the 'Remember Me' functionality then you will need to write your own code to set the cookie/ticket. Something like this (taken from here):

protected void Page_Load()
{
    if (Request.Cookies["username"] == null || Request.Cookies["username"].Value.ToString().Trim() == "")
    {
        Login1.RememberMeSet = true; 
    }
    else
    {
        Login1.UserName = Request.Cookies["username"].Value.ToString().Trim();
        Login1.RememberMeSet = true; 
    }
}
protected void RememberUserLogin()
{
    // Check the remember option for login

    if (Login1.RememberMeSet == true)
    {
        HttpCookie cookie = new HttpCookie("username");
        cookie.Value = Login1.UserName.Trim(); 
        cookie.Expires = DateTime.Now.AddHours(2);

        HttpContext.Current.Response.AppendCookie(cookie);
        Login1.RememberMeSet = true; 

    }
    else if (Login1.RememberMeSet == false)
    {
        HttpContext.Current.Response.Cookies.Remove("username");
        Response.Cookies["username"].Expires = DateTime.Now;
        Login1.RememberMeSet = false; 
    }

}

Just use a simple cookie with 2 weeks expiration date.