It's not the most interesting part of digital photography, but essential if you're not going to lose images. Every storage device fails sooner or later, so you need to make sure you have at least one other copy of your images, preferably more. It doesn't take a lot of kit, just simple external hard drives and a little thought. As a rough guide, here's my workflow:
1. Copy images from sd card to first external hard drive* (I choose not to store any on my laptop itself).
2. Amazon Drive is set to automatically sync with the folder I use for my images, so another copy is created in the cloud.
3. Manually start a Time Machine backup (Apple's backup facility) to a second external hard drive*.
4. Once the processes are finished, my image files are in three places** so I'm comfortable deleting them from the sd card. I then keep additional copies after post-processing of any images for clients or portfolio work, both locally and online.
*There are more comprehensive storage solutions available, such as a NAS (Network Attached Storage) from Synology or Drobo, with built in redundancy (a second copy is automatically created within the system whenever a new file is added).
**An extra measure is to have a third hard drive stored in a different physical location, such as at work or left with a friend, and updated occasionally with new images.