When Zotero is installed in your browser, by default you will see three icons in the top-right hand corner of your toolbar (Firefox) or a red circle Z in the address bar (Chrome) or a button with a red circle Z next to the address bar (Safari).
You can save journal articles in bulk to Zotero by searching a database for the topic you are interested in.
Zotero organizes your research into collections that act like folders. You can add a citation to any number of collections or subcollections.
When you are going to be saving citations for a particular project, you should make a Collection for that project and save everything related to the project in it.
Although, most of the citation information that Zotero captures will be correct, it is always a good idea to check every item's metadata for accuracy and then to correct and/or add data before putting it in a paper. Zotero will accurately import the metadata but the metadata may not be accurate. Check for things like authors' names in all-caps or missing information.
You can edit a citation's metadata by hand by clicking on the text next to the label.