To import items from different kinds of sources into Zotero, you'll click the small icon in the upper right-hand corner of your browser (see the instructions on the right), but the way the icon looks will vary depending on what kind of source you're looking at.
For a database article, you'll see an icon like this:
For a book in a catalog (our own, Google Books, or an online bookstore), you'll see an icon like this:
For a web page, you'll see an icon like this:
For a site with multiple citations on a single page, from which Zotero allows you to pick and choose which to import, you'll see an icon like this:
Your first step will be to go to zotero.org and log in with the username and password you set up.
Then start your research, and once you find an article you want to save, you'll see an icon in the upper-right-hand corner of your browser that looks like a small sheet of paper: You'll find this in approximately the same place whether you're using Chrome or Firefox.
You'll click that icon to save the citation:
The first time you click the icon, you’ll likely see a popup message like this:
At this point, click “Enable Saving to Online Library.” Then you’ll see another popup like the one below. When you see this, choose "Accept Defaults" (this is Zotero "talking" to the database and telling it that it wants to save your citations from now on).
Now you'll see something like this at the bottom of your browser screen, which indicates that the citation is being saved:
Now if you navigate back to zotero.org and choose the "My Library" tab...
...you'll see that your citation has been saved.
When you click into the citation, you can see details about it: citation information drawn from the database, a stable URL from which you can find the article again, and a PDF if one is available: