An Anarchy is when there is no functioning government or leader - so normally no rules to follow. An example is the Somalia anarchy.
This is when one individual has gained power by force, and runs rules that everyone has to follow. Citizens have no voice to express what they want. Examples include Adolf Hitler in Germany, and Kim Jong Un in North Korea.
This is where religious leaders such as priests or popes rule in the name of God. Citizens usually have no say, as it is disrespectful towards their religion. For example, Afghanistan is ruled following Islam religion and laws.
This is when a small group of individuals rule - this is generally depended on wealth or power. This includes the Soviet Union and oligarchy governments in China.
A democracy is when citizens themselves are able to decide who governs the people, by nomination. For example, people in NZ vote for a candidate (from a political party) to represent their area.
A monarchy is when there is one leader - a king or queen. They rule for as long as they are alive, until the crown is inherited by their children. An example includes Queen Elizabeth II, who currently rules Britain.