This video from our friends at Georgia State University will tell you how to get started saving citations to Zotero. Please note that because it's a different university, their Library catalog looks different, but Zotero works exactly the same way no matter where you're using it.
You can also save webpage information to Zotero. This can be hit or miss, as not many webpages have the amount of embedded information that articles and book pages do. This means that often the only information Zotero will be able to pick up about the webpage is the title and perhaps the year it was last updated.
However, one particularly useful thing that Zotero does with webpages is that it saves a screenshot of the webpage. That way, even if you're offline or the page has been updated, you'll see be able to see what it looked like when you saved it.
To save webpage information, the Zotero button will have an icon that looks a little like the article icon, but different. Click that.
As seen in the screenshot below, Zotero didn't capture much information about the webpage. But it did capture a screenshot, which is very important when citing webpages since they change so very often.
Remember that if for some reason Zotero didn't copy the citation info correctly, you can always edit it manually. In the Zotero application, select the item in your library. On the right side of the window, there will be a pane with all the information it collected about the item. To edit it, just click the text and type.
The Zotero connector button will change icons based on what type of source you're looking at. It isn't always 100% accurate, but it can be helpful! The most helpful is when the icon is a folder—this means that there are multiple sources to save on that page, and you can pick and choose which ones you want to save to Zotero.