First, you need ThomasV fingerprint.
gpg --recv-keys 7F9470E6
Or save from
https://pgp.mit.edu/pks/lookup?op=vindex&search=0x2BD5824B7F9470E6 as ThomasV.asc
Go back to Electrum website
https://electrum.org/#download and download Electrum-3.1.2.tar.gz and its signature Electrum-3.1.2.tar.gz.asc
Copy all the 3 files to the same folder, open the terminal and use command 'cd' to navigate to that folder and run these commands.
gpg --import ThomasV.asc
gpg --verify Electrum-3.1.2.tar.gz.asc Electrum-3.1.2.tar.gz
If the message returned says Good signature and that it was signed by ThomasV with a fingerprint that ends with 7F9470E6, then the software is authentic.