Zotero is open-source, and it is easy for anyone to create additional tools to add functionality to the program. Over the years, many plugins have been created that give users the ability to customise Zotero to their needs and preferences.
To install them, the usual procedure is to download the file (with an xpi. extension) to your computer, then go to the Tools -> Plugins, click on the gear on the right, select Install Plugin from File and select the file.
For a complete list of Zotero plugins, click here.
ZoteroPreview adds a Preview tab with a citation preview for the item. You can directly copy and paste the citation.
Another way to preview a citation in all the styles you have in your Zotero is to use the Style Preview pane, a built-in feature of Zotero. Settings menu -> Cite, and click on the Style Preview button. Select an item and click on Refresh.
Zotero Actions & Tags is a plugin for managing tags, with batch processing and the ability to set custom rules.
This plugin can auto-fetch DOIs for new items, shorten DOIs using http://shortdoi.org, and check the validity of DOIs.
A plugin to format item metadata and check for duplicate items when new items are added. It adds shortcuts and a pop-up toolbar to bold or italicise words, automatically adds or corrects the abbreviated title of a journal, automatically corrects certain errors (e.g. importing a document with the item type "web page" and a URL containing the name of a major academic publisher may be an error), automatically adds some missing information.
Zotero Attanger and ZotMoov are plugins that help you manage your attachment files. It allows you to automatically move your attached files to the directory of your choice, inside or outside of Zotero. Both can allow you to store your PDFs on an external server when you reach the limit of the free storage space on the Zotero website.
A sophisticated plugin that can make Zotero a great note manager. Lots of features, but a manual is included.
More details here.