It is less complicates if you are buying a new car. Most of bigger car dealers offer their customers registration of their new car on your behalf (so you will get a new car already with „plate“ and inevitable documentation).
In case of buying older/used car outside big resellers you have to arrange this altogether with previous owner at police. You can arrange it at state administration Client Centre on Tomasikova Street in Bratislava.
For more details on car registration visist:
State administration Client Centre opening hours:
Address: Tomášikova street 46, Bratislava
Monday, Tuesday, Thursday 8:00 to 15:00
Wednesday 8:00 to 17:00
Friday 8:00 to 14:00