In a direct democracy, people vote directly for their leaders. In a representative democracy, people vote for representatives who elect our leaders, but in a direct democracy we skip that step entirely and do it ourselves. Countries like Switzerland use this system. Some people want to abolish the US's electoral college and make it a direct democracy.
Communism
A dictatorship is a form of government totally controlled by one person, or a small group. Dictatorships usually form when a government and or country is in financial straits, or when it is in a time of war. Dictatorships generally don't last that long as the people suffer in these type of governments. Dictators are often assassinated by an unhappy public, which sometimes brings an end to that country's government.
Oligarchy
Republics are governments by the people, for the people. Like a direct democracy, the people in charge are elected by the public. Supreme power is held by an elected leader and his or her representatives. One famous republic is the US. Another famous republic was ancient rome.
Anarchy
Communism itself is an ideology based on equality, but many governments that adopt communism are some of the most unfair. The largest and most famous communist government is the Soviet Union, which lasted from the 1920s-1990s. The people at the top had huge amounts of power and the working class lived in poverty.
An oligarchy is similar to a dictatorship in that much of the power is concentrated with the leaders, but with an oligarchy the power is shared with a small group rather than just one person. Some oligarchys turn into dictatorships when one person in the groups overthrows the rest. This is a common way for dictatorships to form.
Anarchy is a society devoid of rules and government. When governments topple some countries anarchy forms people start breaking laws if no one can enforce them. Some parts of Ukraine have broken down into anarchy as the infrastructure that supports them has collapsed.