As of June 11th 2021, all foreigners temporary/long-term residence permit and relevant commercial health insurance in the Czech Republic can register to get vaccinated against Covid-19. Please note that foreigners have to cover the cost of the vaccine themselves (price for one dose should not exceed CZK 810, no more than CZK 1620 for both doses).
More detailed information can be found on the government´s website related to Covid-19: https://covid.gov.cz/en/situations/register-vaccination/vaccination-self-payers
As for recognition of vaccinations from other countries, the Czech Republic currently has recognition agreements with: Croatia, Hungary, Poland, Austria, Slovakia, Slovenia or Germany. The templates of national certificates can be found here: https://koronavirus.mzcr.cz/vzory-narodnich-certifikatu/.
If you have any questions, please contact the Student Affairs/International Students Office