Historically, the one and only purpose of the safety pilot for someone flying the plane under the hood was to look out for other airplanes and obstructions. You are not an instructor or an evaluator -- just a pair of trained eyes connected by voice to the pilot flying so s/he doen't run into another airplane or an obstacle s/he can't see with the hood on. That's it. The biggest problem with that is resisting the temptation to watch what the hooded pilot is doing and keeping your eyes outside, not inside.
A few years ago, the FAA decided that when operating under IFR, the safety pilot was also there to help make sure the pilot flying didn't do anything improper in the way of IFR procedures, and changed the rule to require that the safety pilot hold an instrument rating when the flight is conducted under IFR. They never said exactly what they consider the safety pilot's additional duties/responsibilities are in that case, so it's something of a vague area which must be decided by the two pilots involved.
And that brings us to the most important issue -- the preflight briefing. Before starting the engine, it's essential that the two pilots involved establish the duties and responsibilities of each so there's no question or confusion in the air. Decide who will be the PIC ultimately responsible for the flight, and what duties will be delegated to the other pilot. Discuss transfer of control procedures, who will handle the radios, how to advise the hooded pilot of traffic, when and how the safety pilot will tell the hooded pilot of other dangers detected, etc. Make sure you both are happy with the other one's view of how this will be done, because the cockpit in flight is no place to hash this out.