The Browser add-on is not a standalone zotero program. It only allows connectivity between the browser, your online or PC based Zotero program and sources of items (eg books, articles, etc) that can be used for referencing.
What does the Browser add on do?
The browser add on (Zotero calls this the "Zotero Connector" is available for Firefox, Edge, Safari and Google chrome. There is some slight differences in functionality for the browser add ons. After you have added it to your browser, it will look at a page and indicate if there is content to save to your standalone computer based account.
Depending on the website, it may be able to download the meta data from a web page and create a reference for it.
So if you are looking at a newspaper site, the add on will web scrape the information for you. So, for example, if the add on is compatable, it will identify the biblio information for the article on display, and also allow you to save the full text of the article.
To download the add on
1) Go to Zotero.org
2) Go to Home > downloads
3) Select install firefox (or whatever one you need) connector
4) You will get a pop up message - select continue to installation
5)Select continue to Installation
6)it will ask for permissions - select add
7)You will get a message saying Zotero was added
8)Go up to the top right of firefox, and select connections
9) You may get a pop up window telling you to download Zotero to your computer, if you haven't already done this.
10) Otherwise, if you want to connect to you online account, you can select that option
11) Once the add on is installed, and you have Zotero active on your computer go to a page you want to save - right click on the page.
You will then see options to add the information click it and it will save the web page as a reference for you.