The first thing to do is go to their website and register for a free account. Registering will allow you to use Zotero to its fullest capabilities, in particular syncing your tool with the online space so that you can access your articles from any computer with an internet connection.
Below is an image of my account, fully synced. I can access files that I have uploaded to this account from any other computer, even if I don't have zotero installed on those computers.
