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.
When using the search box on the Library homepage to look for books, you'll have an option to save multiple entries to your Zotero library. This will be indicated by the Zotero icon looking like a folder.
When you click the folder, it will bring up a window in which you can select all entries, deselect all, or you can pick and choose by clicking the checkboxes next to each item.
If you instead want to view the information for each item individually and then save it to Zotero, you can do that by clicking its title. Then, if you decide to save it, the Zotero icon will look like a book. If you click that, a popup will show telling you the progress of the save (what it will be called in your Zotero library, etc.) Saving should only take a few seconds.
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.