Best Way to Handle Log-Ins

So, I have a site that requires users to log in.  For the past few years, I've been just doing a custom form with 2 text boxes for user name and password with a submit button.  The submit button selects * from Users where User = 'User' and Pass = 'Pass,' and if Reader.Read, set Session("UserName") = reader("UserName")
That's kind of the crude way I came up with to do this because I needed a quick option I knew how to make work.  But now, I want to make sure I'm doing this the "correct" way.  One thing I've been looking at is the asp:LogIn method.
Basically my question is, how does that work?  The examples I've been able to find online basically use the _Authenticate event handler to do exactly what I've been doing all along... which makes the asp:LogIn control a pre-made version of what I already have.  ...with the exception of the "Remember me" check box.  What does that "Remember ...