Haruspicy

Haruspicy, the method the Etruscans used to read entrails and how they learned it.

"Tagetes taught the Etruscans the difficult discipline of haruspicy, the art of divining the future by observing the entrails of sacrificed animals, namely the liver. The haruspex was a priest highly thought of by this people; he was so important in divining the future that his "profession" outlived the Etruscan civilization itself for centuries, after the latter was absorbed in the Roman civilization."

Also see

Extispicium
Augur
Augury
Early Rome

Sources:
(www.isa.it/tuscia/english/history/etrus6.htm) Tuscia
The Art of Haruspicy An article on the Etruscan art, with charts.