You can download the program from zotero.org for both Mac, Pc, Linux and iOS-devices.
When you have completed the installation, you have to check that you have also gotten the 'connectors' for your browser, and for your word processor. For most users, this will happen automatically, but it happens that you will have to do this manually for one or the other - it's quite easy.
On the download page at zotero.org you can find the connectors and guides to installing them, if you have issues.
The connector for your word processor can be 'boosted' from the program Zotero - find the boost-button under Preferences/Cite/Word processors. You may have to reboot for the changes to come into effect.