So you heard WordPress has been updated to 3.6.

Hold on!!! Before you update to the latest version of WordPress 3.6 be sure your theme will support it. Or else you may find your website will not be working correctly when you are done. Double check your plugins also, that they are compatible.

Back up your files.

Be sure to have a back up of your files. Your wordpress database, you know the one where all of your pages and posts are. Also it is a very good idea to back up your entire file structure where your wordpress is installed. If you are unsure of yourself ask your hosting provider or ask the person who put your website together for you.