Before you begin collecting sources, you'll want to configure your Zotero Preferences:
Books and Articles
Zotero senses when you are looking at an article in a database, the New York Times, a book in the library catalog, or at Amazon and allows you to add it to your library with just one click.
To save references to your library, open your Zotero pane (lower right side of the web browser) and look in the address bar for the item's "Save to Zotero" icon in the upper right. The icon image will change from a book, newspaper, article page, or folder depending on the type of resource you are viewing.
Since Zotero has written meta-data translators for sites like Amazon.com, you can look for the book icon at the upper right side of the address bar and click the icon to save the reference to your library.
Search results in databases will include a folder icon in the upper right side of the address bar. Click on the folder in order to choose the search result item(s) (in this case articles) that you would like to save.
The citations and any additional meta-data from the items you are selecting will automatically be brought into your Zotero library, where you can edit all of the attributes, add tags, notes, child items, and create relationships between your resources.
Collecting Sources: Other Websites
If a particular website does not have Zotero translators written to interpret its metadata, try installing Readability, a free Firefox add-on that strips away unnecessary web content to let you focus on the text. According to a ProfHacker article, installing the Readability app makes sites that weren't interpreted by Zotero able to be captured via the Zotero icon in the address bar.
Of course, you can still manually add the reference to your library using these steps:
Click the Zotero button at the bottom right of your browser to access your Zotero pane. Click the "Create New Item from Current Page" button (to the right of the green plus sign) to save a link to the page. This will save a new web page item to your library. You can add information about the author, etc., if you'd like.
This will also attach a snapshot of the page to the citation. Taking a snapshot saves a copy of the page to your computer as it appears at the time the page is being capture. This includes the page's text and images, so if the page is removed later, or if you're offline, you'll still be able to view your copy.
The "Create Item from Current Page" icon is circled below.
You can expand your Zotero storage by using Zotero on a flash drive. Download Portable Firefox and install the Zotero add-on.
For more information, take a look at Zotero's syncing and Portable Firefox documentation.