When organizing you citations in Zotero there are a few different ways that you can do this. One of the easiest ways is by creating folders for your various projects and papers.
To create a folder while using the web based version simply select the "+" symbol. This will then open a new folder and you can name this however you would like.
To add a folder while using the Zotero Application select the folder icon with the green plus sign that is found on the upper left hand side of the screen. Once selected you will be prompted to name you new folder.
Keep in mind that if you have synced your library any folder that you create in the application will be reflected in the web version of Zotero and vise versa.