Certain garages here have MOT [Ministry of Transport] capability, and vehicles are tested by them , but basically they are working for the Ministry of Transport when they test your car, though they make money on the certificate and get a lot of repair work from failures.
In the UK its pretty straightforward , brand new cars need no test for the first 3 years, after that its every year, same for older cars obviously.
Theres all the usual check, lights, steering , suspension, seatbelts, tyres must have a minimum tread of 1.8 mm depth across the width no deep tears etc, bodywork, corrosion etc etc etc.
All cars made after 1991 need to pass a Cat test, before that its a standard gas test, if you go back to pre 65, you can get away with quite a bit.
Test takes about an hour and costs you £50 [$100] if it fails and you take it away, it costs you £25 for a re-test.
All Mot certificates are now registered on the national computer along with your insurance details, so any police car can soon check if your not playing the game.
To drive on the road you then need a Tax Disc [displayed in the front screen] which varies for the size of engine, ie my 1.8 focus is almost £200 per year. [$400] you cant purchase one without valid insurance or mot certificate.
Recently the police are now deployed with hand held number plate readers, details are checked with the computer, just having no tax disc can result in confiscation and the crushing of said vehicle.