Zotero makes it very easy to switch managers. The instructions below are for EndNote, but they easily translate to other systems.
At a most basic level the process is: 1) Export citations as a file in some format from your starting application. 2) Import that file into your new application.
There is a detailed guide from Georgetown University Library at: Migrating Bibliographic Data from RefWorks to Zotero
Note: Folders in RefWorks cannot be moved to Zotero along with your references. In Zotero folders are called collections. You will need to create new collections in Zotero that correspond to your folders in RefWorks if you want to preserve your folder structure.