Saving references is the easiest with the Zotero Connector browser plugin. The plugin simply saves the webpage you are currently on as a reference. Download the plugin, if you hadn't already.
See also Zotero's documentation on how to add items to Zotero.
Zotero Connector identifies the type of the website quite well, e.g. when you are on a journal article landing page, it knows to save it as a journal article reference. In the image below Zotero Connector is saving a book reference.
Image: Zotero Connector is saving a book reference. Click to enlarge.
If Connector doesn't identify the type correctly, the page and its metadata is saved anyway, and you change the type manually in Zotero. See "Editing items" on this page. For example, Zotero saved the blog post below as a Web Page.
Image: Zotero Connector is saving a blog post. Click image to enlarge.
If the page you are visiting has several references (and if Zotero recognizes them as such), you can save multiple references at once. Click the Connector, and choose which references you want to save. Note however, that the reference information is more likely correct, if you save the reference from the original source, instead of e.g. Google Scholar.
Image: Choosing several references in Google Scholar. Click the image to enlarge.
You can also save references as a file, if Zotero Connector doesn't work for some reason.
Most databases have the option to import citations as files. Download the reference as a RIS file and
Whereas with Zotero Connector you can save any webpage as a reference, saving a reference as a file is mostly possible only on journal websites and databases, depending on the publisher and the platform.
Image: Download Citation window in a SAGE journal website. Click the image to enlarge.
Google Scholar doesn't have a direct Zotero export or the option to download a RIS file, but Zotero uses the same file format (RIS) as RefMan, so you can choose RefMan in the Cite window, and open the file in Zotero or download it to your computer, as described above. Zotero Connector (see above) does this in a much more simple way, though.
Image: Cite window in Google Scholar. Click the image to enlarge.
When you have selected a reference in the center pane, you can view and edit the bibliographic information and change the "Item Type" via the Info tab of the right-hand pane. Most fields can be clicked and edited. Changes are saved automatically as they are made.
Image: editing a reference in Zotero. Click the image to enlarge.
For example, the book article below didn't have all relevant information available on the article landing page, which is why Zotero Connector couldn't retrieve it anywhere. You can add missing data such as editors and pages yourself.
Image: Editing a reference and adding information in Zotero. Click to enlarge.