Zotero can make files available to users in two ways: by storing a copy or by linking to them. Storing a copy will add that file to the Zotero data directory, separate from the original file. Linking will simply refer to the original file without creating a copy or changing its location. Stored files will be included with any file sync, while linked files will remain only links. Any type of file can be added to the Zotero library, either on its own or associated with another item.
Copies and Links
To store a copy of a file, you can simply drag the file from your file browser into the Zotero pane, dropping it into a collection in the leftmost column, or in amongst the library items in the center column. Dropping the file on a collection or between items will create the copy as a standalone item. Dropping it on an existing library item will attach the file to that item. These associated files can be accessed by clicking on the arrow that will appear next to the item.
A stored copy of a file can also be created by right-clicking on a link to a file in Firefox (or in the case of an image, on the image itself), then selecting “Save Link [or Image] as Zotero Snapshot”.
Both stored copies and links can be created by clicking on the New Item button and selecting the appropriate option, “Store Copy of File” or “Link to File”, though these will always be created as standalone items.
Attachments
You can add attachments to items by clicking on the New Child Attachment button, its the one that looks like a paperclip. This will reveal different options for attaching links and files in the New Child Attachment menu. Through these options you can store a new copy of or link to a file on your computer, as well as save a link to or snapshot of the current Firefox page. Associations can also be created by dragging a standalone child item onto an existing regular item.
File Storage
All files stored in the Zotero library are kept in a folder within the Firefox profile directory (unless another location is specified in the Advanced preference tab). Each file has its own subdirectory within the Storage folder, named with a random 8-character string. As such, it is probably inadvisable to attempt to navigate to these files in your file browser. Below this level, though, the files are named intelligibly, so it is possible at least to run a search for them. Easier than all this, however, is accessing these files directly through Zotero. Selecting the item in Zotero and clicking the Show File button in the right column will open your file browser and take you right to the file.