If you want to view source info before saving it to Zotero, you can do that by clicking its title.
Then, if you decide to save it, the Zotero icon will look like an article, book, film reel, or whatever type of source you're looking at. If you click that, a popup will show telling you the progress of the save (what it will be called in your Zotero library, whether it saved an attached PDF, etc.). Saving should only take a few seconds.
When viewing a full list of search results in a database, the Library catalog, etc., 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 sources, deselect all, or you can pick and choose by clicking the checkboxes next to each item.
Remember that if for some reason Zotero didn't copy the citation info correctly, you can always edit it manually: