The four rules myth is the myth that gentiles who become believes in the Messiah only have to follow four rules. The support for this myth comes from Acts 15:19-20 which states that the new believers are only required to (1) abstain from foods sacrificed to idols, (2) from sexual immorality, (3) from consuming strangled meat and (4) from consuming blood. Often times, these are claimed to be the only rules that Christians need to follow, period. But making such a claim is quite the intellectual blunder. To drive home the point, prohibitions against murder and theft is not on this list, and sexual immorality is left undefined.
In order to understand the passage in question, we need to understand the context of what's going on. Starting in verse one, we read that a certain group of people (known as the "Circumcision Group") were claiming that you must be circumcised in order to be saved. This is in stark contrast to what Jesus himself said in passages like John 11:25-26, which clearly state that salvation is by faith alone. In verse 4, we see that some of the believing Pharisees said the same thing, and added that they must be required to keep the Law of Moses (the Law that God gave through Moses). The implication is that unless they are circumcised and immediately keep the entire Law that they themselves were not able to keep, then the Gentiles cannot be saved. This caused quite the debate which was finally settled in verses 7-11 by Peter pointing out the fact that the Gentiles were accepted "as-is" when they believed.
The entire chapter of Acts 15 is about the requirements for salvation, but also tells us what we must do once we are saved. In verse 21, which is the verse directly after the four rules, we find the reason that only 4 rules are given to the new believers. The reason is because the new believers are expected to attend Synagogue every Sabbath (Saturday) where they would learn the Law gradually over the course of a year. The Jews read through the entire Law of God every year, dividing it up into many portions with a different portion being read each week. The four rules that were given to these new believers were to address the most important issues of morality that would have been present during that time. They would learn the rest as they grew in Messiah.
Some would have you believe that Acts 15:21 means that the Gentiles would not be going to Synagogue every Sabbath to learn the Law. But this goes contrary to what the Bible says about keeping the Law by faith; and loving/knowing God by keeping his commands. See Obedience vs Salvation by Works for more info on this subject. So if the Gentiles were not expected to go to the Synagogue every Sabbath where they would learn the Law, they would never come to know God or know what loving God is. Furthermore, since righteousness is obedience to the Law [Romans 2:13] and is by faith [Romans 2:21-22], if they did not learn the Law or obey it, then they would be disqualified from being righteous.
On one final note, the Bible treats knowing and doing as synonymous. That means that those who learn the Law also practice what has been written in the Law. You cannot know the Law without practicing it.