If you'd like to use Zotero to create an annotated bibliography in APA or Chicago style, you can use a custom citation style designed specifically to output annotations.
To install one of these custom styles, first ensure that the Zotero app is open on your desktop, then choose one of the following styles from the Zotero Style Repository. When you're at the Zotero Style Repository, click on the title of the style and Zotero should automatically install it for you.
If the style doesn't automatically install, go to your Zotero Preferences menu (Zotero > Preferences on a Mac, Edit > Preferences on a PC), then navigate to the Cite menu and click on Get Additional Styles and search for the style you want to install.
Just like it does with any other citation style, Zotero will use the metadata you include for each item in your library to build your bibliography. These custom styles for annotated bibliographies will also include annotations in your bibliography, as long as the annotation is inserted in the correct metadata field in your Zotero library.
For the Chicago Manual of Style 17th edition (note, annotated bibliography) style, add annotations to the source's Extra field in Zotero.
For the American Psychological Association 7th edition (annotated bibliography) style, insert annotations into the Extra field.
For the American Psychological Association 7th edition (with abstract) style, insert annotations into the Abstract field.
Generated annotated bibliographies is no different than generating normal bibliographies with Zotero. If you are using Zotero's word processor plugin to cite sources as you write, simply change your document preferences to use one of the installed annotated bibliography styles and Zotero will include annotations when you generate the bibliography on your document.
However, since most annotated bibliographies are standalone documents, it's perhaps easiest to collect all of your bibliography's sources into a new collection (see Adding Items to your Library), then right-click on the collection title and select Create Bibliography from Collection.
Then, select your annotated bibliography citation style from the list and ensure that Copy to Clipboard is selected. Click OK.
Now you can paste in your annotated bibliography anywhere you can paste in text--a Word document, Google Doc, email, etc.