Zotero gives you a number of tools to organize your data. Familiarize yourself with the options available before you start organizing your records.
There are also several ways to find specific records in your library.
Create collections (folders) and use them to organize your citations. Collections can be made for subjects, subdivisions in your bibliography, or as reminders for you to follow up.
Use the folder icon (upper left in the Zotero toolbar) to create new collections. To create a subcollection, right click (or two finger click on a Mac) on the parent folder and pick "New Subcollection".
Click and drag citations into the appropriate folders. Individual records can be in multiple collections or subcollections.
Also, if you select a folder before adding a record to your library, it will automatically add it to that folder.
You can create one or more notes related to your record. Use these to keep track of Interlibrary Loan requests, books you have checked out, the locations where you are storing the book, storing citation information in original script, etc.
Tagging can help you retrieve records. You can create tags for important people or concepts. Once you have used a tag, it will show up as an option when you start typing. This allows you to reuse tags and improve retrieval. Tags will be retrieved when searching your library.
Sometimes Zotero brings in subject terms from the databases and adds them as tags. Don't be surprised when you find that your record already contains tags!
The related tab is a great way to tie records from the same source together. Use them to link records for book chapters to the record for the book. As you type in the related tab, Zotero will suggest related records.