I don't have a complete list of all the measures taken, but in large strokes, the following things happened:
- schools were closed very soon after the first cases of covid-19 were discovered;
- large gatherings of people were prohibited (not more than 100, then after some period not more than 50);
- a state of emergency was declared when there were relatively few cases of infections compared to the population number;
- a lot of local districts started to take actions on their own, like closing public parks.
- the private sector also took action. Companies encouraged employees to work from home, sporting events were canceled, stores changed their program or limit the number of shoppers at any given time, hypermarkets started to disinfect their shopping carts and protect their cashiers with glass windows, trains in the subway station would pull only one by one at the platform to limit the number of passengers that would gather together.
- because a state of emergency was declared, new laws were passed to control what people were doing. First there were restrictions to be on the streets between 22:00 and 06:00. This lasted for a few days, then restrictions were put in place all day. Now or example you are not allowed to exit the home unless for some specific reasons like buying food, seek medical help, take care of elderly people, go to work, and a few others. People above 65 are not allowed to go out of their home unless they have an emergency. For other activities they are only allowed to go out between 11:00 and 13:00. Stores reinforce this by allowing only the elderly to shop in that time interval. Now all parks are closed. And groups of more than 3 people are disallowed. All shops and malls that don't sell food or things you need to survive were closed.
These are a few things that happened since the whole covid-19 cases started to happen in Romania.
Now, to your question. Because we are in a state of emergency the law was changed to account for the pandemic situation. If you have returned from abroad you need to go into self-isolation or you are placed under quarantine (for 14 days if I remember correctly). You are not allowed to leave your house and friends, family or couriers must provide you with food and supplies. You don't interact with them, they just leave them at the door. If you do not respect these measures, the fines are now very large, up to 20000 RON (more than 4000 EUR), and you can also go to jail. If you breach self-isolation or quarantine and you are discovered, you are being placed under military guard so you don't do it again.
Now, with that being said, you can't really monitor 200000 people or keep them in check. There are controls, but you can't really keep them isolated. Many were discovered wondering the streets, going to parties, visiting friends, etc by the authorities. It helps I guess that there is some panic and people will report those that they know came from abroad and are not sitting put (mothers have reported their children to the authorities, for examples).
So basically that's what's happening right now. We have lower cases of infections than other countries because everyone reacted quickly and took measures before things were bad. Because movement is restricted this limits contact between persons. People also isolated themselves in the houses by precaution before the state of emergency was declared (for example, a few days before the state of emergency was declared, people hit the stores and bought all the flour and yeast, rice, canned produce, etc to stay in home for weeks) because of worry, fear, panic.
For further reference, some details on the infection in Romania:
(on the left, in red are the total confirmed cases, in yellow are persons under quarantine, blue is people in isolation at home, in gray are the number of deceased people)
My belief is that authorities panicked when they saw what was happening in Italy for example (many Romanians live there and return for Easter Holiday each year) so they took harsh measures before it was needed. It seems it helped. Although they also took some bad decisions like limiting access to information (in the name of having it from official sources). I don't remember exactly, but I think that link above is from independently collected data, as authorities no longer report cases per district, but only globally.
EDIT: as a response to your comment I've looked up a few examples in the media:
1. In the first day of restrictions of circulation, 5,621 persons who did not comply with the measures were fined 7,404,297 RON (1,531,965 EUR). That's an average of 1,317 RON (272 EUR) per person.
2. In later news, the number of people who did not comply with the restrictions of circulation and were fined increased to 23,973, and an amount of 31,400,000 RON (6,496,730 EUR). That's an average of 1309 RON (270 EUR) per person. The same news mentions that for 209 persons a criminal record was opened and 4,235 were fined for non-compliance with the isolation/quarantine measures.
3. The news in point 2 did not mention how much the fines were for those that did not comply with isolation/quarantine, but in older news, 10 days ago, on the Ministry of Health's website it was stated that 1,835,000 RON (379,665 EUR) of fines were applied to 120 persons for not respecting the measure of isolation. That's an average of 15,291 RON (3,163 EUR) per person.
So the fines for breaking isolation/quarantine are quite large (plus getting a criminal record for more severe situations). For reference, the minimum net wage in Romania is 1,346 RON (278 EUR) while the average net wage is 3,189 RON (659 EUR). So for a large number of people, the fines are quite large.