The following are a list of the key types of democracy. They do no represent every type of democracy that there is. For a more complete list, see the Wikipedia page here.
This is the type of democracy that you would be most familiar with. Virtually all democracies across the world are representative. What this means is that the people vote for candidates (or sometimes political parties directly) that represent their views at free and fair elections. The winners of elections make decisions on behalf of the people.
Direct democracy (or "pure democracy")
This is the type of democracy where people get to vote directly on issues. Switzerland is famous for direct democracy as it is the only national government that regularly uses direct democracy. Direct democracy is to some extent used by democracies across the world. The recent Australian Same Sex Marriage Postal Survey was an (unusual) example of direct democracy.
Deliberation means that the “will of the people” is arrived at by a process in which people weigh competing reasons under good conditions. Basically this means the public should have an opportunity to learn about a topic, discuss it with others, question experts and have an equal say before exercising their vote. Deliberation must facilitate discussion among the public that is free from distortions of unequal political power, such as power one obtains through economic wealth or the support of interest groups.
Delegative democracy (or "liquid democracy")
Delegation is a system that allows everyone to participate in votes and hold ultimate control whilst also allowing people to delegate their vote to someone else that they trust to make a decision on their behalf.
It is sort of like representative democracy but the key difference is that in delegative democracy the people are always capable of taking back their delegation if they are not happy with the decision that has been made.
Digital democracy (or e-democracy)
This term is quite broad, it incorporates any use of technology in democracy. To date, digital democracy has taken one of two forms, either:
augmentation of the current voting system - like electronic voting that occurs in some elections; and
enhancement of the current political system - like online platforms that challenge the way that the conventional political system works.