Jeff will correct me if necessary, but here's my understanding: For attacks with class 1 or 2 melee weapons, no surprize roll is needed; the target only need be "unaware" of the attack. (The referee could rule that a target in the midst of melee with the assassin's companions might be unaware of the assassin hiding and moving silently behind him.) If the attack hits (with a +4 bonus), check the Assassination table for chance of instant death. Even if instant death does not result, normal backstab damage applies, with a multiple based on the assassin's level.
Assassins also can assassinate with a missile weapon, but only at short range, and only against a target who is not engaged in combat and does not expect danger. In other respects, the attack is resolved as above.