Pre-Hogwarts education consisted of a child learning how to do magic from their parents. If their parents or any other immediate relatives are unavaliable, the child may be port-keyed to another family who would have a child at the same learning level as the child in question. So small tutoring groups would form and often friendships and partnerships were a result. This is how Gryffindor, Ravenclaw, Hufflepuff, and Slytherin all knew each other was through such an arrangement.
As stated in the premise, the law over wizard-kind is generally set by the family in charge (who has the most money and power). Aurors are those witches/wizards appointed by the head of the clan in charge to carry out their will. So aurors are more so marshalls than actual policemen.
The following are a list of families that have a high influence in wizard society.
Gryffindor is currently the family of the most power thus rule wizard affairs. They dwell in the Yorkshire area typically. At this moment in time, the patriarch of the family is Godric's father, Alasdair. He took over for his father, who was killed by an opponant. The Gryffindors have been the family in charge for about 8 generations. The family preaches tolerance for both wizards and muggles. No senseless muggle killing! Even so, the Gryffindors tend to look on muggles with a degree of pity and protect them like how some activists nowadays protect endangered species.
Alasdair's great-great-grandmother Dorrin ran family affairs for a time and established the Wizengamot, the beginnings of the ministry. It was her attempt to establish some sort of law over wizard kind. She wasn't able to get all the heads of family to sign an agreement to follow such rules, but it was an attempt to bring the family together. Such a thought of unifying wizard-kind was abandoned. However, at this current point in time, Alasdair is rumored to attempting to unite wizards across the islands under one law making/enforcing body. Such attempts are in the beginning stages.
Alasdair had married Melwyn of Weasley and the couple had ten children. The heir to Gryffindor was not Godric but his older brother Blythe. The order of children went in the following order; Gwendolyn, Blythe, Godric, Milyan, Briar, Sterenn, Tristan, Vevila, Cecily, and William.
As a side note, Weasleys were once noble wizards but time wore that away. It really doesn't matter if the Weasley's in the current saga are decendents of Melwyn and Alasdair or not. Anyway, moving on!
Longbottom. This family as well as some of their family connections, are located in the Lancastershire are of Britain and are known for their charity towards muggles. Although they don't outwardly say what they are, they don't mind helping muggles using magic, stealthily of course! Some families look down on this practice as it has already gotten a few of them into trouble. The Gryffindor line overlook this fact since Alasdair's sister married into the family. Some families make snide remarks that the Longbottoms are so eccentric is because it is always a matriarch who oversees family actions. However, most families look at the Longbottoms as being noble and brave for risking their own necks to help the less fortunate.
Malfoy. Ah yes, this family never dies. The Malfoys probably once upon a time originated in Normandy and settled on the island. For as long as anyone remembers, this family had always been cruel towards muggles and smug about their magic ability. Their wish is to pretty much rule over both wizard and muggle worlds that there should be no separation. Muggles would be used like house elves, like servants and nothing else. At one point, the Malfoys were the family in charge. They had overthrown the Blacks and they were overthrown by the Gryffindors. Since the family had an obsession with keeping the blood pure, incest was not uncommon and except for a few individuals, the Malfoys are weak-minded as of late.
Black. This family is probably the biggest threat to the Gryffindor family. This lineage goes far back and 'ruled' Britain for at least 100 years. This family shows a similar trend to the Malfoys except they viewed muggles like rats; annoying but no matter how many you kill, they keep on coming back. Some wizards of this family, or allied with this family, like to hunt muggles for the fun of it or curse them for just the fun of it.
Other families not listed are allied or married into one of these big families. Most follow the will of Gryffindor. And if they don't, Gryffindor's Aurors will get you.
Any questions? Anything you want to add? Please respond to this post.