The password is stored in
/etc/shadow and you can try to confirm it with john the ripper.
I am not sure if posting tutorials for john are allowed here, if so I can write one easily enough, but if not a google search will show you how.
Last I looked, John needed a patch, but the bug report on launchpad seemed to indicate that the patch was incorporated into the repos, so I would try the un-patched version first (I know, lazy =) ).
Short of john,
su - test_user -> enter password.
Brief tutorial on john the ripper:
sudo apt-get install john
Prepare the working database (I made a user "test" with a weak password for this example).
sudo unshadow /etc/passwd /etc/shadow > password.db
Loaded 2 password hashes with 2 different salts (generic crypt(3) [?/64])
Remaining 1 password hash
guesses: 0 time: 0:00:00:03 0% (2) c/s: 222 trying: monday - emily
As you can see, john cracked the weak password in 0.03 seconds, my user password is too strong for john so I aborted it with Crtl + c
Show the password
john --show password.db
1 password hash cracked, 1 left
Here we see the user "test" with the password "testing"