I will take the bait since I was one of those that inhaled lot of tear gas on 10th of August 2018 and I am also following the local politics in Romania.

Paul Johnson's answer is what I feel is the right answer legally and democratically. However, this also requires time (at least until the next elections). In Romania's case, you can also choose one of the opposition parties (PNL, USR, RO+ etc.).

they can do it and the people pretty much have to watch (especially
if some protest ends badly like the one in Romania from August the
10th)... Then wait for the next elections.

Despite the 10th of August protests ending bad for the protesters, it also ended bad for the Government (source) due to international reactions:

The events on 10 August also lead to international reactions. Austrian
Chancellor Sebastian Kurz strongly condemned the "violent
confrontations in Bucharest, at which numerous protesters and
journalists were injured" (..) In the context of the Mechanism for
Cooperation and Verification, the European Commission follows the
events with worry and gives an increased importance to the
independence of the judiciary system and of the fight against
corruption.

MCV was particularly bad for Romania in 2018 and it is the first time when Bulgaria has a real hope to access Schengen Area, while Romania does not.

Also, the main party in power in Romania (the Social-Democrats) significantly lost in vote intentions for next elections (EU Parliament and local Parliament) [citation needed] and recently lost majority within the Chamber of Deputies.

The opposition can use all these to gain political advantage in the elections to come.

So, my answer to your question is:

The common citizen can protest against what he/she sees as undemocratic government decisions. Typically there are some effects since the country is far from being isolated (e.g. Romania is both within EU and NATO).

In Romania's case there was significant political pressure from both US and EU.

Most every democracy has free speech protections. The key to defending democratic principles is to use the hell out of them. Start a YouTube channel. Write a blog. Submit articles to web sites who share your opinions. Get active on social media. Start a local group with like-minded individuals. Make rational, passionate arguments for all to see. Use your creative talents to artistically illustrate a point. Use your charisma to win people over to your way of thinking.

If you're right and your opposition is wrong, people will see it. People will be persuaded, even if it takes a long time. Fight for the long game. If you're the one who's wrong, make sure you have the humility and the self-reflection to own up to it. That will endear you to other people.

The strength of a democracy is not found in the leaders who control its institutions, but whether or not those leaders properly fear for their jobs if they screw up those institutions.

The bare minimum: VOTE

As provided in Paul Johnson's answer, is to join the political party. That answer is specific to becoming an activist. However, there are many more things that can be done.

Run for an elected office yourself. In many countries, there are lower level, more obscure, or more localized elected positions that are more easily obtainable.

Then, if not joining the politics directly, there is joining a career field that allows influence over politics. Journalism is a popular one.

Frequently, people forget about think tanks, watchdog groups, charities, or non-profit groups. Some of these are paid careers, some are voluntary.

Ultimately, the gateway for democratic governments is voting. You either cast your vote for someone you believe speaks for you or you convince others to give you their vote to speak on their behalf. There is little that can be done between votes from the outside.

Any leverage is applied to an elected politician through pressure or concern that they would lose their position, essentially. If a politician is swaying from their base, a protest or vocalization about the dissatisfaction usually occur. However, politicians wont change their tune unless it is more beneficial for them to listen than to keep their course. If pressure alone isn't enough, it escalates tension and civil unrest. The threats are usually to a politicians career, as in not being re-elected. Sometimes that devolves into more dire consequences.

Edit: Clarification to the language on leverage per comment suggestion.

Change the Political Culture!

Even if political leaders have just won an election, they usually worry about what will happen in the next election. So they worry about the political climate. They will not follow through with decisions if they are widely unpopular.

What you can do is to do your small bit in influencing the public debate and culture. If a person in a subway train says something you consider outrageous, say that's wrong! If a person at the supermarket checkout comments on a newspaper headline you consider outrageous, say that's wrong! If a person posts something online you consider outrageous, vote it down and post that's wrong! If a person in a bar says something you consider outrageous, say that's wrong!

If people say or write outrageous things and nobody contradicts, then everybody starts to think that is normal. It will encourage those people to say and do even more outrageous things, and it will discourage others to speak out because nobody likes to be in the minority. That's an uncomfortable place to be in any debate and also in one's own mind, but if nobody speaks up against outrages how can you find out if you really are in a minority?

Depending on where you live, it might make sense to hold back if you fear that it could lead to a brawl. Or if you had a hard day at work and you don't want that argument now. But the way politics work, silence is interpreted as consent. Don't be silent.

The voice of a single voter won't mean much. The voices of many voters mean a lot. How will you find out if you are one of many if you don't talk?

Other answers have discussed various kinds of activism. However, while these methods have focused on time commitments like volunteering, protesting, phone banks, etc, there is another less direct form of activism, namely financial.

This can be a monetary contribution directly to a particular candidate, or to a group whose cause you support, or to more generic party organizations. But by donating money you help support a cause you believe in. (Note: this answer is focused on small time donations, from "the common citizen")

This doesn't have to be a lot of money to make a difference. A few examples. The NRA was quite successful, mostly being funded through individual contributions (let's keep this simple and say, only consider before the turn of the century). Bernie Sanders received the majority (57%) of his 2016 funds from small time donors (<$200). And most recently, Susan Collin's as-yet-unknown opponent has received over 3.7 million dollars, with over $1.7 million of that coming from people only donating $20.20.

I disagree with you that citizens have no power in a democracy aside from voting and protest. Voting is quite powerful. If you want political power beyond the vote, you can write an influential book or conduct research on topics you are knowledgeable and passionate about. Politicians often use the works of others to inform their decisions. If you do not have sufficient knowledge or skills to be influential in this way, you can still influence others in your social circles by demonstrating your views to them. Try to live out your principles truthfully and with conviction. Then people will take notice, and may even incorporate your ways into their worldview. Democracy is a way to balance political power across people, but some are still more influential than others.

Read

Find out what others think of what "democracy principles" means. A lot of great scholars have written a lot of great things about these concepts. Being from the US, myself, I would naturally defer to the founding fathers of the US in a great many cases, but they are by no means the only people who have written on the topic!

Think

Why do we have democratic principles? What are the underlying goals of them? Why do we have a process which isn't 100% perfectly in line with those principles? There are practical reasons for this. Understand when we benefit from these deviations. They aren't always bad. Think it through. Don't assume anyone else tells you the right answer.

Talk

Let ideas get shared. You, as a single citizen, really can't do all that much to change the course of a nation. Arguably, it is designed that way on purpose. However, by sharing ideas, you can align with others and a large number of citizens can often do things to shape the nation that small numbers cannot. Many of the examples of becoming an activist fit in this category. Share ideas. Get ideas from others. Learn and grow.

Organise a protest with a convergence of multiple actors. If there is sufficient anger among the public, it will escalate and become powerful enough to be taken seriously by the elite (like it just happened in France). It's a risk worth taking. If it does not escalate, then there is no sufficient fuel yet for it.

There are some good answers here but I didn't see any mention of the ultimate power of the citizen, at least in the United States. Here we have the ability to recall elected officials. Get enough people to sign a petition and a special election will be called to decide if the official should get recalled out of office.

I'll answer with a personal example, as someone who prefers living in a free society but was born in one of the least democratic countries in the world. The solution is...

Emigration

If you look at our society from a wider perspective, there's absolutely no reason for a person to feel obligated to support a given country simply because they were born there. If a person from New Zealand is willing to adapt to Belgian society and Belgium is willing to grant this person a residency permit, there's no reason why this person couldn't forever leave their birth country and feel no allegiance to any government except the one in Brussels.

Therefore as a person who's goal is to live in a more democratic society, you can always just pack your bags and go for greener pastures. Which is exactly what tens of millions of people around the world are doing as they're trying to find a better life for themselves and their families. As a bonus, leaving your country of birth will result in brain drain and the odds of it eventually being forced to reform are increased by a tiny percentage.

Encourage your country to join a supra-national organisation such as the EU or the Council of Europe (which has nothing to do with the EU but is the governing body for the European Convention on Human Rights) which limit the undemocratic options that your national government can take unless it is prepared to break international law and abrogate treaties.

In corrupt democratic systems (and also more widely), a good option is not to vote. This is a protest suggesting the democratic system is illegitimate/corrupt. There is a good analysis of the consequences of abstention here.

Related, voting null or blank is another form of protest. An analysis of this is here.