To import photo files from your hard disk into Shotwell, just drag them from your file browser into the Shotwell window.
Alternatively, click File ▸ Import From Folder and select the folder containing the photos you want to import.
Shotwell will ask whether you want to copy the photo files to your library folder (usually this is the Pictures folder in your home directory) or to import them in place without copying the files.
If you hold down Ctrl while dragging photos in, Shotwell will copy the photos into your library folder without prompting. Similarly, if you hold down Ctrl+Shift while dragging photos in, Shotwell will import the photos without copying them.
Once the import is complete, you can select Last Import in the sidebar to see all photos successfully imported. The Events list will also show new entries for the dates corresponding to the imported photos.