This question is fairly broad and a little ambiguous, so I think you are going to get a variety of answers. There are many unwritten factors which could be applied here, but one thing I think is probably universally true is that when a law is considered "morally wrong" it creates controversy.
You ask, who determines if it is right or wrong? Well, therein lies controversy.
You ask, what is done to change it and how does change happen? More controversy.
Our legislature does not tend to pass laws that would be universally considered immoral. Therefore, people choose sides, those who are for something and those who are against it, or say it is "immoral." Then, they fight about it. They fight in court, they fight in the media, they fight on the floor of the House and the Senate. Some fight on Youtube and Facebook. Discussions go back and forth. Examples are drawn, pictures are drawn, sometimes even movies are made. Speeches are made. There are protests and rallies and parades. And there is more arguing.
Think about it this way: this country would probably never allow murder for the sake of murder. We can almost universally agree that cold-blooded killing is morally wrong. Abortion, however, is much disputed. And even today, we don't really have a resolution.
If a law is morally wrong, people will begin to stop following it. Usually there will only be a few really strong-minded souls who want to stand on their own moral code at first, but they will have sympathizers. Before long, the people making the immoral laws will have their hands full.
The law can be seen as a codified or formalized version of a culture's morality or moral thinking. Legal or illegal status can generally be understood as an extension of perceived morality.
There are some issues though that present us with complex or contradictory cases. For example, certain corporate practices intended to evade the payment of taxes are technically legal yet ethically wrong (when considered in an ethical light).
This particular issue is relevant to the question of who should decide whether or not to change the law. While governments want to close loopholes that allow this kind of tax evasion, corporations argue that the health of the company is important to national strength.
Who has the right to decide in this case?
This really depends on where you are. In most dictatorships, for example, you accept the laws, regardless of whether they are unjust. It's either that or go to prison or be oppressed in some other way. In a place like the US, you protest or engage in some other form of political expression to try to get the laws changed.