1. Back up the iPhoto Library to the Hard Drive.
Most Simple Back Up:
Drag the iPhoto Library from your Pictures Folder to another Disk. This will make a copy on that disk.
Slightly more complex: Use an app that will do incremental back ups. This is a very good way to work. The first time you run the back up the app will make a complete copy of the Library. Thereafter it will update the back up with the changes you have made. That makes subsequent back ups much faster. Many of these apps also have scheduling capabilities: So set it up and it will do the back up automatically.
Example of such apps: Chronosync- but there are many others. Search on MacUpdateor the App Store
2. Open it to check it works. To choose a Library to open:
Hold down the option (or alt) key and launch iPhoto. From the resulting menu select 'Choose Library'
3. Export the pictures from iPhoto to the external drive: File -> Export and use the image viewer as Old Toad suggests.
This User Tip
has details of the options in the Export dialogue.