Hi tsfexhibit,
I agree with lehrerfreund here. Generally speaking, the best practice for upgrading software that powers a website is to do so in a test environment first, where any issues that arise don’t immediately cause a panic. Often we see folks just set up a subdomain like http://upgradetest.domain.com where they fully upgrade their site before moving those changes over to the live site. You’ll want to work with your host to get that set up.
You could also set up a local test environment on your Mac or PC. Products like MAMP and WAMP really help you if you’re not the server admin type.
Then, like lehrerfreund suggested, once you have your site working in the test environment, upgrade that installation. After you’ve verified that the test environment upgrade worked, push those same changes to the live site, essentially reversing the process you used to create the test environment.
Once you get the site working on the test environment, you might even consider creating a multi-server config.php file like Matt Weinberg suggests in this tutorial.
Best of luck!