Go to http://www.zotero.org/ and click the big red Download button at the top-right.
You’ll get a warning message that reads, “Firefox prevented this site (www.zotero.org) from asking you to install software on your computer.”
Click the Allow button to the right of the message
A small window will pop up, then click the Install button.
A small pop-up window asks you to restart Firefox to complete your changes. Press Restart Firefox button.
Congratulations! Zotero is now installed in your Firefox browser. You could see Zotero icon on the bottom right corner of your screen 
You can also add Zotero to the top toolbar by following View -> Toolbars -> Customize and scroll down to find the Zotero icon 
and drag it to the toolbar. Both Zotero icons can be clicked to switch on/off the Zotero interface. You can also open/close Zotero by following Tools -> Zotero or using short cut: Ctrl + Alt + Z.