Raspbian 5/5/2015, the version I am working with, comes with read support for NTFS. Presumably earlier versions over the past year or two probably have this as well, but much past 2 years, I don't think they do.
On a default install of Raspbian, the OS will automount your NTFS drive as read-only to /media with the NTFS volume name as a folder name. This makes things easy to see, find, and understand. eEpecially if you're primarily a Windows user or new to Linux.
To get read and write access, you have to install some software, in this case, just 1 package: ntfs-3g. Some older instructions may tell you to use ntfsprogs, but there's no need for that. To find out the difference, see this page/article/question: Which package to use for NTFS? NTFS-3G, NTFSPROGS? [closed] There are no answers, but the comments are good.
Before you install ntfs-3g, you'll need to update apt-get. You can do that with this command:
sudo apt-get update
I'm not sure why, but the package links for apt-get are out of date in regards to ntfs-3g. Once you update apt-get, then you can install ntfs-3g:
sudo apt-get install ntfs-3g
Then you will need to power cycle the Raspberry Pi. I'm not yet sure why there is a difference between a reboot and a power cycle, but you must power cycle the Raspberry Pi. That means turn it off, wait 5+ seconds, then turn it back on. Since my drive was powered by the same USB hub-thingey as my Pi, I used the switch to turn off the Pi and the drive, waited 5 seconds, and then turned both of them back on.
That's all you need to do!
To test, in the GUI, I opened up File Manager, saw that the drive was mounted in /media, and created a new directory somewhere. It succeeded. If you had tried to do that before all of this, then that would have failed with an error message about insufficient privileges.