You will need to choose the citation style that Zotero will use when inserting citations or creating bibliographies. This is done in Microsoft Word. Go to Add-Ins, find the gear icon, and set your Document Preferences for citation style (for example to Chicago Manual of Style).
Zotero offers word processing plugins for Word and OpenOffice. The plugin adds a Zotero toolbar to your word processor that allows you to add citations to your document while you write.
To add a citation, click the first button ("Insert Citation") on the toolbar. Select the reference you want to cite and click OK. Zotero will add the citation at your cursor.
At the end of your paper, click the third button ("Insert Bibliography"). Your bibliography will appear, and new citations will be added automatically. Change bibliographic styles with the last button on the toolbar ("Set Doc Prefs").
It's easy to create a bibliography from your Zotero library.
Select the references or collections you want to include. Hold the control key and click to select multiple items. Right-click one of the selected items and choose Create Bibliography. Choose the bibliographic style you want, and select the output format: Save as RTF or HTML, copy to clipboard or print. (The RTF file format is compatible with all word processors.)
Or you can just drag and drop references from Zotero into your document! They'll turn into fully formatted citations. This works with any word processor including Google Docs.
Go to http://www.zotero.org/styles and find and download the style called Chicago Manual of Style (note, annotated bibliography)
Put your annotation in the Extra field, towards the bottom of the Info tab on the left. (You can cut-and-paste from a Note if you've already made an annotation there.)
Select the items for your bibliography in the middle window and right-click to Create Bibliography from Selected Items. In the dialogue box, choose Chicago Manual of Style (note, annotated bibliography) - this is the style you installed in the first step. Save as RTF, then you can open the file with Word. You may need to adjust the spacing, but your annotation should appear after the bibliographic citation for each item.
You can use Zotero to take notes on what you're reading -- it's a great way to track your reactions to the writer's ideas, and to note where you might want to include the information in your paper. If you do that, you'll always know where you got your ideas, and it will be very difficult to accidentally plagiarize something. See http://www.zotero.org/support/notes
You can also highlight text on a web page and automatically copy it to Zotero. See Creating Notes While Browsing.
The Notes field is very large, so don't worry about writing too much.