I'm new to web design and just started a business a month ago. I have a good grasp on a lot of things but I am curious about this particular site....

www.ultimate-guitar.com

My question is how do they update all of those links on the front page so often? What system are they using for that because I can't image someone is actually sitting there updating all those links every hour.

You have maybe already guessed that the site most likely uses a content management system (CMS), which is a way to manage content by storing it in a database and providing users and administrators an interface that they use to add, delete, or modify the data. Wordpress is an example of a CMS for bloggers. You used this forum's CMS (vBulletin) when you posted your question.

Ultimate-guitar.com appears to be mostly user-submitted content. The front page of the site probably has a server-side script that automatically pulls the most recent data from each category (reviews, news, etc.) and formats it as the HTML page that you see in your browser.

If you want to know for sure what is going on with that particular site, you can ask them directly.