Neither Ubuntu nor Mint come with out-of-the-box support for the fingerprint reader. This is quite surprising as it wasn't too hard to get working on Arch Linux completely manually. Thanks to a fingerprint-gui PPA, though, it is not difficult to get going in either of the distros.
Also, be sure to check out the other slightly better integrated method in my other article.
Now, before we go on, not that the solution is butt-ugly. The interface has nothing in common with anything else you have on your OS, and I'm seriously considering doing the manual install as on Arch Linux, simply to avoid watching at this ugliness.
Adding the PPA and packages
Before you can do anything, you have to download the packages. First add the PPA from your terminal application:
sudo add-apt-repository ppa:fingerprint/fingerprint-gui sudo apt-get update
After the above has finished, you can install the necessary packages with the following command:
sudo apt-get install libbsapi policykit-1-fingerprint-gui fingerprint-gui
Reboot your computer.
Enrolling your fingerprints
After your computer has rebooted, you will need to enroll your fingerprints. Open the main menu, and find the Fingerprint GUI application.
Under the Finger tab, you can select the finger(s) you want to enroll, and click Next at the bottom of the window to enroll. Each finger is scanned three times.
Using the fingerprints
Using fingerprints to log in, or when you issue
sudo command, is completely automatic. A small (and ugly) window comes up telling you to swipe your finger.
As you can see, it looks like it came from another planet, and a not very nice experience. It also dumps a bunch of GTK warnings to the terminal, which makes it a not so good choice.
Currently, I am not aware of any alternatives. I will, however, try to follow the fprint instructions on ArchWiki, and see if those can be adapted to Mint. It's a much more pleasant experience, and doesn't look out of place at all.