Do good and avoid evil
Natural Law focusses on actions, asking whether an action is good or bad - is it in accord with human nature? At first glance, it is easy to apply Natural Law to issues like Abortion and Euthanasia.
Natural Law and abortion
From the Primary Precept 'Protect and preserve the innocent' we get a secondary precept 'Do not abort'. This is an absolute moral rule - abortion is always a wrong act. The Catholic Church reasons in this way, and condemns abortion in all instances.
The moral debate here will focus on the details. For example, is the use of the pill (not the 'morning after pill' taken a day or so after sex to prevent the embryo attaching, but the birth control pill taken throughout the month to prevent conception in the first place) tantamount to abortion? A professor in America is one of many who claims that science has demonstrated that "birth control pills usually prevent pregnancy, but sometimes they cause an abortion."
Also, does Natural Law require you to believe that a foetus is a human being from the moment of conception? If you don't agree with the Catholic Church on this (and the history of this belief is a fascinating one - they used to think it was much later, and changed their teaching because of inaccurate scientific beliefs that have since been shown to be wrong), you would be able to hold that early abortions do not contradict the Primary Precept 'Protect and preserve the innocent'.
Natural Law and Euthanasia
Euthanasia also needs careful definition. If you talk to any doctor or nurse, they will admit that medical staff have always made decisions about patients who are very ill with no hope of recovery that many would call 'passive euthanasia'. To know whether these decisions contradict the Primary Precepts, you need to know what would be considered to go against the precept 'Protect and preserve the innocent'.
There is much debate about what is considered 'withdrawl of treatment'. If you stop feeding someone, is that withdrawing treatment or something more than that. In a nutshell, natural law theorists would agree that it is wrong to kill a person, but they would disagree about what 'killing a person' included.