What tools should I look into to approach taking ownership of website?

I'm part of an organization that has a website, and I'm taking over that website to manage it for them. I have lots of experience with HTML, CSS, and JS, but no experience doing website admin. The only information I have right now is that the previous admin used Dreamweaver.

What information should I seek out in order to approach administrating a site in a scenario like this? The previous admin said that you can download software and use it to just take over administration of the existing site. How should I approach this?