Tails transitioned to a new signing key between Tails 1.3 (February 24) and Tails 1.3.1 (March 31). If you had the previous signing key, make sure to import and verify the new signing key.

You need to have GnuPG installed. GnuPG is the common OpenPGP implementation for Linux: it is installed by default under Debian, Ubuntu, Tails and many other distributions.

Get the Tails signing key

First, download Tails signing key:

Tails signing key

Open a terminal and import Tails signing key with the following commands:

cd [the directory in which you downloaded the key]
gpg --keyid-format long --import tails-signing.key

The output should tell you that the key was imported:

gpg: key DBB802B258ACD84F: public key "Tails developers (offline long-term identity key) <tails@boum.org>" imported
gpg: Total number processed: 1
gpg:               imported: 1  (RSA: 1)

If you had already imported Tails signing key in the past, the output should tell you that the key was not changed:

gpg: key DBB802B258ACD84F: "Tails developers (offline long-term identity key) <tails@boum.org>" not changed
gpg: Total number processed: 1
gpg:              unchanged: 1

If you are shown the following message at the end of the output:

gpg: no ultimately trusted keys found

Analyse the other messages as usual: this extra message doesn't relate to the Tails signing key that you downloaded and usually means that you didn't create an OpenPGP key for yourself yet, which of no importance to verify the ISO image.

Verify the ISO image

Now, download the cryptographic signature corresponding to the ISO image you want to verify and save it in the same folder as the ISO image:

Tails 1.4.1 signature

Then, start the cryptographic verification, it can take several minutes:

cd [the ISO image directory]
gpg --keyid-format long --verify tails-i386-1.4.1.iso.sig tails-i386-1.4.1.iso

If the ISO image is correct the output will tell you that the signature is good:

pg: Signature made Sun 08 Feb 2015 08:17:03 PM UTC
gpg:                using RSA key 3C83DCB52F699C56
gpg: Good signature from "Tails developers (offline long-term identity key) <tails@boum.org>" [unknown]
Primary key fingerprint: A490 D0F4 D311 A415 3E2B  B7CA DBB8 02B2 58AC D84F
     Subkey fingerprint: BA2C 222F 44AC 00ED 9899  3893 98FE C6BC 752A 3DB6

or:

pg: Signature made Sun 08 Feb 2015 08:17:03 PM UTC
gpg:                using RSA key 98FEC6BC752A3DB6
gpg: Good signature from "Tails developers (offline long-term identity key) <tails@boum.org>" [unknown]
Primary key fingerprint: A490 D0F4 D311 A415 3E2B  B7CA DBB8 02B2 58AC D84F
     Subkey fingerprint: A509 1F72 C746 BA6B 163D  1C18 3C83 DCB5 2F69 9C56

If you see the following warning:

gpg: WARNING: This key is not certified with a trusted signature!
gpg:          There is no indication that the signature belongs to the owner.
Primary key fingerprint: A490 D0F4 D311 A415 3E2B  B7CA DBB8 02B2 58AC D84F

Then the ISO image is still correct, and valid according to the Tails signing key that you downloaded. This warning is related to the trust that you put in the Tails signing key. See, Trusting Tails signing key. To remove this warning you would have to personally sign the Tails signing key with your own key.

If the ISO image is not correct the output will tell you that the signature is bad:

gpg: Signature made Sat 30 Apr 2015 10:53:23 AM CEST
gpg:                using RSA key DBB802B258ACD84F
gpg: BAD signature from "Tails developers (offline long-term identity key) <tails@boum.org>"