Fr. Gregory Pine, O.P., answered this question:
We know the natural law by virtue of the inclinations to which it gives arise. Because we are substance, we are inclined to the preservation of existence; because we are an animal, we are inclined to the procreation and education of children; because we are a rational animal, we are inclined to know the truth about God, live peaceably in society, to shun ignorance, to avoid offending those with whom we live.
Not intended as an exhaustive list. But because of what we are, we incline toward certain things. Our nature gives rise spontaneously to certain loves, because love recognizes what is suited to a substance.
How do we register that? Part of it is culturally conditioned. It can be blotted out of the heart of man, but not in a way that is thoroughly devastating.
But you can be better or worse at knowing the natural law, depending on where you live, when you live, according to your social circumstances.
He continues, answering the second part of the question: how does acting contrary to our nature damage us after the effects of original sin?
Acting contrary to our nature damages after the effects of original sin insofar that it further obscures from us the natural law (and the divine law, for that matter), because it poses an obstacle both intellectually and volitionally towards the attainment of our end.
So, when we act contrary to our nature, we will develop vices. Vices become operative habits where we tend to a good lessor or to a good that excludes our ultimate good, making it easier for us to act contrary to our nature.
The highest end, or purpose, for us as human beings is beatitudo: commonly translated as happiness, but better understood as fulfilment through other-regarding action. In other words, love. The consequences of original sin (or, for those who don’t like that phrase, the consequences of our fallen nature – which cannot be denied), is that we fail to love. We fail to reach our highest end, or purpose.
We fail at the greatest commandment:
Matthew 22: 36 Master, which is the great commandment in the law?
37 Jesus said unto him, Thou shalt love the Lord thy God with all thy heart, and with all thy soul, and with all thy mind. 38 This is the first and great commandment. 39 And the second is like unto it, Thou shalt love thy neighbour as thyself.
40 On these two commandments hang all the law and the prophets.
Natural law should be best understood as an ethic. This differentiates it from natural rights, which can be enforced via legal prohibition and defended by physical force if necessary.
Natural law commands that I act charitably toward others; no one has a natural right to force me to do so. Natural rights are limited, fundamentally, to the protection of life and liberty. One can think of this as the non-aggression principle.
Hence, natural rights (or the non-aggression principle) do not offer a full moral or ethical code. That is to be found in natural law. Teaching natural law is the role of the family and the Christian Church (and should be the role of education and universities); enforcing natural rights is the responsibility of every individual and whatever governance institutions they jointly and willingly establish.
A society that teaches and lives under a natural law ethic can move toward liberty. There is no other way.