Once you've downloaded and opened Zotero, you will notice My Library in the upper left.  As you add citations to Zotero, they will all save to My Library.  

However, if you would like to further organize by project, course, or theme, you can add new collections.

Citations with then be added to both your selected collection and to My Library

Email Zotero Support
Scholarly Research Services at the Libraries
 

1. Select the add citation button in the toolbar of your Zotero library
   
    
2. Select what type of bibliographic citation you want to enter in your Zotero library, i.e. Book, Book Section, Journal Article etc . . .
   
    
3. Begin entering bibliographic information in the right frame of your Zotero library