As with all ethical theories, it is useful to know the key features of a theory in order to apply it. Most exam questions focus on the authority of the conscience - whether it is God given and ought to be obeyed. However, by focussing on the specific features of each theory, you can say particular things about whether to follow the conscience. There are also interactive diagrams on War and the Conscience and Sex and the Conscience.
For example, Newman says the conscience knows by intuition. This is a way around the naturalistic fallacy - how do you move from is to ought? Utilitarians say we desire pleasure (or some revised goal - the meeting of preferences, interests etc.), therefore we ought to bring about the greatest good. This is an example of the naturalistic fallacy. Situation Ethics avoids the fallacy with the positivist position that we should do the most loving thing (this is an assertion - you either accept it or reject it, but there's no point arguing about it as it is an assumption).
If you ask whether we should value pigs, monkeys etc. intrinsically, Utilitarians would ask "Do they feel pain?" or "Do they have interests?", but they can't give any justification for saying we should value interests. Newman would simply say that we have a God-given intuition that is the 'voice of God'. If we listen to that voice, we would know whether to eat meat, experiment on monkeys etc.
The downside of this position is, clearly, that our intuitions vary greatly - this undermines the idea that the conscience is God-given at all.
Freud rejects the idea that we should follow the conscience. He doesn't believe in objective morality at all. Freud would attempt to describe and understand behaviour. At best he might talk about what was healthy or unhealthy. He would not say what we should or should not do.
For example, when fighting a war, some people are very happy to kill enemy soldiers. This may be because society has reinforced negative images of the enemy, supported by propoganda and a xenophobic atmosphere among soldiers. Other soldiers may feel traumatised when required to kill enemy soldiers. This may be because of ideas about the sanctity of life imposed by parents and others in the early years. Freud's explanations undermine the idea that we should follow our conscience. Instead, a healthy person should allow the ego to control actions.
It is interesting that, despite appearing as opposing theories, Aquinas' theory of conscience is very similar to what Freud might say a healthy person should do. Aquinas thinks you should use your God-given ability to reason. Even Butler, who sees the conscience deciding between self love and benevolence, is similar to the Freudian id and superego. The main difference is that the superego isn't love of others - rather, fear of social disapproval.
So, Freud might urge you to ignore feelings of guilt and act rationally - whilst Newman might argue that the guilt is a God-given intuition that you have done wrong, Butler and Aquinas would agree with acting rationally.