So, let's get started (storing)! I'll reference Dropbox for iOS here, but it is available on Android and Blackberry devices, too.
Jump over to your respective App Store/Google Play/App World and download the FREE Dropbox app. The best part about Dropbox, and you'll notice many other service offer this, is that you can setup an new account right from your smartphone. Dropbox syncs between your device, and computer, and needs an account set up to get everything started.
Once you're past new account creation, Dropbox acts as a metaphysical hard drive, ready for you to create folders, upload and share files. When Dropbox initially sets up, you can elect to automatically upload camera photos - either wi-fi or wi-fi + cell data. I suggest wi-fi only, to save on any cell data overages, plus the files typically upload faster on wi-fi.
Once you're all set up, and presented with an empty space, now's time to upload some files. The best feature is being able to send important email attachments to your Dropbox folder. Say there is an Excel file that you received that needs to be saved. On all devices, you will be given options when you click an attachment. Now that you have Dropbox installed, the "send to/open with Dropbox" option will be present.
Open in Dropbox leads you to the save to Dropbox option. Dropbox is capable of previewing most documents and then has an option to save the file.
Just hit that Save button, and you're done! You've successfully saved a file to Dropbox, and jumped into cloud computer. So simple, it shouldn't be allowed, right? Simplicity and ease of use is what makes technology so great today. You don't need to be a computer whiz, just geeky or savvy enough to understand the tools already available.