The online version of Zotero is quite robust. In order to use it you must create a Zotero account and sync your Zotero library to Zotero.org (if you have access to a webdav server you can use that, but it is a bit more limited - for example, you will be able to upload PDF documents, but not webpage screenshots). This is also where you can create and manage Zotero Groups (although the actual moving around of records between your Zotero library and a group library happens in your Zotero library on your desk/laptop in Firefox or Zotero Standalone).
Your Zotero library on Zotero.org lets you add records via cut and paste, edit records (including adding notes and uploading attachments), and cite works using about 8 commonly used citation styles. If you use the Zotero bookmarklet, anything you add is automatically added to your Zotero.org library, and then synched to your desk/laptop Zotero library.
If you just sync your Zotero record (including notes) it will not cost you anything. If you choose to also sync attachments (i.e. PDFs and webpage screenshotes) you get 300MB for free, then there is a charge. I pay $20.00 /yer for 2GB - this pays for my stoage and helps to support Zotero (its probably the most valuable $20 I spend in a year ;-) Syncing attachments means you have access to your article PDFs, etc. where ever you are, as long as you have an Internet connection.
Note: mobile device apps such as PaperShip or ZotPad use your content in Zotero.org and provide it with added value. For more information on this, see the Zotero on Mobile Devices tab on this guide.