By actual developments, we will inform you about the measures against the Corona Virus in Hungary.
UPDATE February 12th 2021
UPDATE December 14th 2020: Due to the extremely worsening pandemic situation with an unprecedented number of cases in Hungary, the government has further tightened the measures again.
Private gatherings are limited to 10 people, except for funerals, which are limited to 50 people. All shops and service providers must close at 7:00 p.m. Every customer must wear a mask. The age-depending shopping times are abolished again. At night there is a curfew between 8:00 p.m. and 5:00 a.m. The gastronomy has to close, only pick-up is allowed, hotels are only allowed to accommodate business travellers. Leisure and sports facilities are closed to the public. Schools up to 8th grade will remain open, all other educational institutions will switch to digital teaching. The public administration has partly switched its activities to electronic traffic or, unless it is a matter of compelling and non-postponable matters, switched to making appointments, partly requires health declarations or has not made any restrictions. You should inform yourself in advance at the authority. Public utilities have individually drawn up their own rules to avoid customer contact.
Throughout the country, a minimum distance must be kept in public from people who do not live in the same household, in the most publicly accessible buildings, as well as means of transport, it is mandatory to cover your mouth and nose with an approved mask, scarves or other coverings are no longer allowed. Penalties have been introduced for those who do not wear a mask or who wear it in such a way that their mouth and nose are not completely covered.
UPDATE February 12th 2021: Hungary has closed its borders again in principle at least until February 2021. Exceptions are citizens from Poland, Slovakia and the Czech Republic, they are allowed to enter the country with a negative test result that is not older than five days.
Hungarians and anyone, who has a registered or permanent residence in Hungary and can prove these facts by means of Hungarian documents (e.g. registration card with address card, permanent residence card with address card), as well as their family members, are also allowed to enter. Quarantine is ordered for each of these travellers.
Anyone who shows symptoms at the border is quarantined in a state facility, whoever shows no symptoms, is sent to quarantine at home for 10 days, which is checked several times a day by the police. The quarantine at home can be shortened by two negative PCR tests, which must be taken at least two days apart; the costs are borne by the traveller. Foreign test results are only recognised as the first test if they come from a laboratory in a Schengen member state, the USA and Canada and are issued in Hungarian or English. Anyone who can officially prove that they have survived a corona infection in the last six months may enter the country without quarantine or a test.
Furthermore, exemption permits for business travellers, for the purpose of travel to judicial and official investigations or the participation in sport events can be granted within a narrow framework. The permit must be issued by the national police before departure.
Citizens of neighbouring countries and Hungarians living in neighbouring countries are allowed to commute to Hungary without quarantine, the same applies to Hungarians who commute to neighbouring countries. This rule does not apply to foreigners living in neighbouring countries.
Movement of goods and transit traffic are possible, but also subject to strict conditions.
DEPARTURES from Hungary are always possible from the Hungarian point of view, provided that the destination country does not prohibit entry. More and more countries see travelling to Hungary as a risk, some expressly warn. To the best of our knowledge Austria, Belgium, Germany, the Netherlands, and all parts of the United Kingdom have classified all of Hungary as a high-risk area. According to the respective regulations, every traveller must on return inform the relevant authorities and go in quarantine or be tested. As far as we know Switzerland hasn't classified Hungary as high-risk area. This information does not mean that countries not mentioned have not classified Hungary or parts of it as a high-risk area! 
These measures can be changed at any time, the list is not complete and does not constitute legal advice about what is allowed and what is not. 
Stay healthy or if you get this wish too late we wish you a speedy recovery!