Every person who intends to use their vehicle in the Czech Republic and whose stay in the Czech Republic last longer than 185 days in the applicable calendar year, has to register it at the applicable municipal authority of a municipality with extended powers. Road vehicles registered in the Czech Republic have to have a vehicle insurance contract, they are subject to regular technical examinations checking the technical condition of the vehicle, with regular emission measurement. In general, it is not allowed to register imported cars older than 8 years in the Czech Republic.
Motor vehicles imported from non EU/EFTA countries have to undergo technical examination (Roadworthinness test) prior to their registration in the Czech Republic (see chapter 5.3.3.b Technical examination). You have to get a Vehicle Liability Insurance prior to car registration. File an application.
I you stay more than 185 days of residence in Czech Republic.
Good to know
Information Publication for Foreigners Czech Republic (in English, Ukrainian, Russian, Vietnamese and Mongolian): http://www.mvcr.cz/mvcren/article/information-for-foreigners-in-the-czech-republic.aspx
Vehicle operation and registration is regulated by Civil Code, Act No. 56/2001: https://portal.gov.cz/app/zakony/zakon.jsp?page=0&nr=56~2F2001~20Sb.&rpp=15#seznam (in Czech, see §6 for list of documents necessary for registration)
You can use services of private companies specializing on registering imported vehicles.
At any municipal authority of a municipality with extended powers. List of municipalities with extended powers (in Czech): http://portal.uur.cz/spravni-usporadani-cr-organy-uzemniho-planovani/obce.asp