You can set up a group and invite other people to contribute to the group's library. See the Zotero documentation to learn how.
See the short video (2:39) on creating group libraries on YouTube.
Zotero is free! Zotero allows you to collect your research, both citations and full text documents (pdfs). You have the ability to organize the research however you like. Later, you can integrate Zotero into Google Docs or MS Word to help you make proper citations and a bibliographies. To get started go to the Zotero site to download the app.
Try this short video (12:40) about using Zotero.
This is a very good training video from the library at the Illinois Institute of Technology.