Question: I have a moveable and closable jquery pop-up notification box. It works well aside from the fact that it pops up every time the page is loaded. What method would I need to implement to allow a user to permanently (or at least semi permanently) close the pop-up box?

If I need to use cookies how would I tie a cookie to a specific action like closing the div?

Answer: 
You could simply use client side cookies: <http://www.w3schools.com/js/js_cookies.asp>

If the user doesn't have a cookie present, display box;
If the user has the cookie present and cookie specifies the user has already closed the box, keep it closed; etc..

It's simple, and doesn't put any extra weight on the server, you can also set a large expiry date if you want the popup not to show on theusers next visit for example. 

Although this does depend on what it's for as sessions may also be another way of handling this. (Sessions may mean that if the user comes back the next day for instance, the popup will show again depending on how it's set up)
session would be another candidate and its secure than cookies. And you don't have to do anything else than setting a variable on loading popup on first time and check afterwards if that variable is set or not.