I was thinking of  getting a usb 3.0 external drive to back up all my songs and all my samples.  Is this the best way to do that?  

It's one way.

In the end the most important things about backups are that you make frequent backups in the first place and you can restore your data from the backup if necessary.

Me, I'm paranoid. So data gets backed up from the SSD I use for tracking to a USB drive, which in turn gets backed up to another. I use the operating system backup routines to shove most data onto network storage, but DAWs can churn out a lot of data very quickly, which clogs up the router if backed up that way, and it's much quicker to use USB3 than even a Gigabit/802.11ac network.

I used to backup to a single drive with the extra copies made on DVD, but hard drive space is so cheap nowadays it's more economical to use extra USB drives.

Microsoft's free synctoy is a usefull tool for making backups. It's officially a Windows7 application but works for me on Win8.1.

I recommend you consider keeping backed up data offsite, as one forum member had an entire studio cleaned out, including backups from 10 years of projects.
 
I picked up a USB 6 TB external backup drive for less than $200, and LOVE it.
 
Of course, my mom had a Life Alert device for a whole year before we discovered she had never taken it out of the box, so DO use whatever backup device/approach you end up getting. :)
 
Bob Bone
 

The best backup is the one you actually make.

I use OneDrive now for my offsite backups of actual songs and I have about 7 drives I use for everything else on-site.
 
The issue I'm having at the moment is doing backups of libraries/installers/etc. I find I'll buy something like a Konakt library and forget to update my backup for sometimes a month. I'm currently looking into some new folder mirroring software that I can run at the end of the day to make sure everything is up to date. The problem I've had in the past, especially with manually moving things, is that it takes too long to go through every single file in Windows to see what's new or changed because of the amount of files some of these sample libraries have in them.

Before backing up, always make sure there's enough room.

It starts with how your store the original files. 
Most people here use a DATA drive for their projects. Everything to do with your projects is stored per folder per project. So it's then a simple matter to back up that entire drive manually or with backup software. 
 
I have a second data drive in the computer and then an external drive. 
The internal back up I perform by using "save as" and pointing it there. 
The external drive I drag and drop my "album' folders as work progresses and I date them. I never delete anything. 
With command center we now have a back up of all our software and plug ins so I no longer worry about that stuff. 
Any third party plug ins are kept on external drives. 
 
Every couple of months I dump my external drive to another computer off site. 
 
For automated back ups I use this free software..  Easeus  ToDo   It's just as good as the paid versions so save your money
http://www.easeus.com/backup-software/?ad&gclid=Cj0KEQjwv467BRCbkMvs5O3kioUBEiQAGDZHL3-qOJ9eCxJrO9hb48Ufbo8kM1dqfL3RHRbPyCDTyqEaAhd08P8HAQ
 
 
 

Thanks for the link Cactus. :)

I use Acronis, a USB3 dock with SATA drives and a couple of NAS drives.
 
Acronis runs 3 jobs every night:
1.  Windows; drive C to the USB dock.
2.  Everything else to the USB dock.
3.  All audio project folders to NAS.  This duplicates the audio project backup done as part of (2).
 

Offsite. If you use a USB drive don't leave it with the DAW. If you nee convincing read this.
 
At the moment I have a NAS drive in a different building to the DAW which contains one set of backups,  A combination of Acronis file backups and system drive image and a mirror file system kept in sync with SyncToy.
 
As a further line of defence against hardware failure I have everything backed up to a USB drive using Acronis file backups. This drive does sit next to the DAW.
 
I like the mirror file system as it is not dependent on any software or compression. SyncToy just add convenience.