The world does not, as far as I know, have any democratic governments. We have republics (and a few monarchies), where some elite, a congress/president or a parliament/prime minister, have privileged political authority, i.e. authority to actually govern. Some republics deserve the name of democratic republics, where all citizens have (more or less) equal voice in privileging the governing elite. Years of gerrymandering and the legally privileged duopoly of the Democratic and Republican parties (never mind the economic power the capitalist and professional-managerial classes use to influence elections) cast into serious doubt whether the United States republic is actually a democratic republic.
In contrast, as I define it, a democracy has no one with privileged political authority. The people govern themselves. The kind of radical socialist vanguard party must support democracy.
Although a democracy will often use majorities to decide issues, a democracy is not the sovereignty of the majority. A democracy must have limits on the will of the majority. Although the people might decide on additional limitations, a democracy must have institutions that prevent a majority from disenfranchising any minority. No one may legitimately barred or limited from participating in the political process as an equal.
Second, institutions and practices must exist to devolve power away from the center, i.e. to localities and regions, rather than the nation (or the world) as a whole. For the people to govern themselves, they should preferably not be governed by people far away, who do not share their interests. There are certain issues that must be governed by the center (notably macroeconomic policy), but it should be institutionally difficult to centralize and easy to regionalize and localize.
All governing institutions in a democracy must be absolutely transparent. Secrets must be limited in only the most extreme cases. (The technical details of military hardware is one example: the people gain nothing important by knowing exactly how to construct a nuclear bomb.) Not even the majority may arbitrarily keep secrets from the minority.
A reasonable template for an institution that can thwart the will of the majority when it acts undemocratically is the institution of supreme judicial authority with the power of judicial review, such as the Supreme Court of the United States. Note that the Supreme Court has been exceptionally effective at preserving the United States' specifically capitalist republic against the threat socialism, but has been flexible enough at times to yield when the socialist pressure proved too strong. People who condemn the Supreme Court for having a poor history of upholding individual rights fundamentally misunderstand the Court's role in a capitalist republic: their role is to preserve capitalism against the majority of the people or their trustees. The role of the Supreme Court can be easily replicated to protect a democracy.
(No political regime is foolproof; if enough people try hard enough and long enough, they can undermine and corrupt a democracy, just like they can and have undermine and corrupt any regime. Sometimes to the benefit of humanity: undermining and corrupting monarchism and feudalism was a Good Thing. However, institutions can slow the process of corruption enough that a democracy does not fall "by accident" or happenstance.)
Implementing an actual democracy presents technical challenges, but we can surmount these challenges. There are a variety of options.
One possibility is to just let everyone vote on everything. Such a method would have been impossible before, but today we have the internet and sophisticated privacy-preserving and identity-establishing encryption and authentication technology.
This approach poses two political issues that cannot be solved technologically. First, the problem of harassment and intimidation, well known today on the internet. This problem can probably be ameliorated by a blend of anonymity and identity: we can establish a medium for political discussion that protects the physical anonymity of individuals, but establishes a "political" identity. Anyone can see all of a citizen's political contributions, but it is nearly impossible to tie that political identity to their personal identity (e.g. where they live and work). Additionally, this medium would probably require some form of institutional moderation.
The more important political issue is establishing and maintaining a consistent focus, to keep the people's individual voices from becoming mere noise. I don't know how to fix this problem, hence I prefer other solutions.
Another possibility is delegated democracy: people elect delegates, who take on the actual work of forming public policy. The difference between a democratic delegate and a republican trustee is that while the delegates provide a point of focus, they are not autonomous. The people can recall their delegates at any time, and might possibly retain the power of changing their delegates' policies directly. Hence delegates to not have privileged political authority, although they will almost certainly have unusual political influence.