Download and install Zotero from the Zotero website.
There are different versions for each operating system: Windows, Mac, or Linux.
Register for a cloud-based Zotero account to sync/back up your work.
This will also allow you to access your library from any internet-enabled device.
The mobile version of Zotero allows you to access and edit your Zotero library on your tablet or mobile phone.
Word processor plugins allow you to cite as you write and create bibliographies.
To get started with plugins, check out the following links: