In general, the term "direct democracy" usually refers to citizens making policy and law decisions in person, without going through representatives and legislatures. The classic example of this is the New England Town Meeting where anyone from the town who wants to show up to debate and vote on town policy can do so. Until recently, this worked for scores of communities, but low attendance at many modern town meetings has raised questions about how effectively democratic they actually are.
More recent direct democracy proposals tend to focus on voting schemes (usually high tech) that would allow widespread, virtually continual voting by millions of citizens on whatever proposals surfaced. While useful in building up a buffet of voting methodologies for possible use in other contexts, the lack of organized public deliberation about the issues in question makes such proposals look more like opinion polls than exercises of citizenship. Wise solutions to public problems won't likely come off the top of a hundred million heads.
A third approach to direct democracy -- the "initiative process" adapted by a number of states -- allows anyone to propose a law which, if they can get enough of their fellow citizens to co-sponsor it (usually by signing petitions), can be voted on by the entire electorate in the next election. While apparently empowering the grassroots, this process has in many instances been co-opted by special interest groups, especially monied interests who put initiatives on the ballot to increase their wealth and power in the guise of public benefit -- or to confuse voters about competing initiatives that actually come from the grassroots. Since the monied interests have more resources to hire petition-signature-gatherers and to run powerful advertising campaigns based on extensive marketing surveys and expert PR advice (sometimes very devious, last minute blitzes that can't be answered before the election), there's a real question about how democratic existing initiative processes are. Furthermore, such processes offer no more deliberation than the unproductive media debates that characterize most political campaigns.
Useful definition note: "It would be helpful for us to use "initiatives" for proposals by citizens, and "referenda" to mean proposals "referred" for a citizen vote by legislators, instead of using referendum generically to mean either." -- Evan Ravitz, http://www.vote.org.
For an intelligent proposal for a national initiative process, see National Initiative for Democracy.
For an international academic site focused on direct democracy see C2D - Research and Documentation Centre on Direct Democracy
For a critique that supports having citizens engage in major public deliberations to advise legislatures -- but not to pass their own legislation -- see Referenda.