The question is how much well-informed citizens need to be to exercise their democratic rights. The answer depends on theories of democracy. The duty of citizens to be well-informed can be very demanding or not demanding at all. Some theories even require moral duty not to vote. I explain these three views in the following.
J.S. Mill's theory can be argued to be very demanding. In Considerations on Representative Government, Mill posits the thesis of the inequivalence of the peoples. The thesis states that the people of democracy are intelligent and active while the people of a benevolent despot are vapid and torpid. The thesis then entails that, even if the outcomes of the benevolent despot and democracy are the same in terms of promoting the public good, there is reason to choose democracy. According to Mill, democratic citizens are active and intelligent since, to exercise their rights to vote, the people of democracy will have to study political issues and agenda in search of the public good. For this reason, Mill called democracy the school of public spirit. To ensure this, Mill ponders on public voting that people can see how each others voted. Mill infamously proposed plural voting (that the educated should have more votes than the uneducated) to ensure that voting results reflect the public good.
Many theories of voting are not as demanding as Mill's. Reasons vary, however. I offer two scholarly arguments for the reason. One is to view the democratic decision making process as a machine. That is, by merely implementing universal and uniformly-weighted franchise, correct answer for the public good will rise to the top. The idea is most strongly supported by Condorcet Jury Theorem, which states that, if each voter is more likely to vote correctly, and independently, then the majority will find the correct answer with certainty as the number of voters increases. James Surowiecki popularized this idea with The Wisdom of Crowds. Under this view, individuals can just vote based on what they already know, and there is no need to be well informed. StackExchage and Quora utilize this wisdom of crowd to find the truth (or knowledge).
The other reason is based on non-epistemic nature of democratic decisions. This view used to be popular thanks to the contribution of social choice theories. The premise for this view is that the core of democratic decisions is empty (non-epistemic due to cyclicity). Then why should we vote? Their answer is similar to the way moral anti-realists explain our moral responses: "Hooray" or "Boo." We vote to approve or disapprove policies or representatives. Under this view, voting is like cheering for your favorite football team, and thus unnecessary is being well-informed. A San Diegan would cheer for Chargers however poorly they performed in the games.
The third view is that it is morally impermissible for uninformed citizens to vote. This view is articulated by Jason Brennan in his The Ethics of Voting. To him, voting is to find the correct answer for public policies and thus ignorance will get in the way in this pursuit of the truth. The argument clearly assumes the correct answer and can be unpersuasive to political skeptics.
