The command-line way
Make sure the drive/partition you would like to attach is attached to your system and is turned on.
This guide is taken from here (it is for 12.04, but should work for other versions of Ubuntu) and bits from here.
Press Ctrl + Alt + T on your keyboard to open Terminal and type:
sudo blkid
This will list the drives on your system, with handle labels, where available.
Take note of the UUID of the drive you wish to automatically mount.
Now the "fstab" file needs editing:
sudo gedit /etc/fstab
OR
sudo nano /etc/fstab
Add this line to the bottom of the file, replacing the UUID with your noted UUID and choose a mount point name (the space character is created by using "\040" in the fstab):
UUID=xxxxxxxxxxx /mnt/Your\040Chosen\040Name ntfs-3g defaults,windows_names,locale=en_US.utf8 0 0
Also replace the local to one suitable for your location and language if you are not in the USA. You can find your locale by typing in the terminal:
locale
The "ntfs-3g" (a Kernel module) is a lower level software tool in almost all GNU/Linux distributions.
Save the file and close it.
Now type this into the terminal:
sudo mkdir "/mnt/Your Chosen Name"
Next, make yourself the owner of the mount point by typing:
sudo chown <username> "/mnt/Your Chosen Name"
Replacing with your username (your username is always lower-case). This will prevent other users from touching it.
Restart your computer and enjoy!