Travelers arriving in Uzbekistan are required to have valid passport and visa. Also, all foreigners arriving in Uzbekistan are required to be registered at Immigration Department of the Ministry of Internal Affairs (Office of Entry, Exit and Citizenship - OVIR) within 3 days. Even if Sunday & Saturday are considered as weekends they are also counted in this 3-day time. Each time when you move from one city to another you have to do it.
But this rule mainly concerns the people who arrive in Uzbekistan for staying for longer periods and people who will be traveling in Uzbekistan off Beaten Tracks and who will stay in guesthouses. People applying for registration pay from a few dollars to a few hundreds of dollars following the duration of their stay in Uzbekistan. Staying in Uzbekistan without registration may lead to fines or deportation of the visitors.
All the travelers who will be staying in hotels do not need to do anything and this is the hotel which does the OVIR Registration for travelers.
As a rule, each time when you arrive at a hotel you give your passport to the receptionists and they take a copy of your passport for registering at OVIR/Police. They may keep your passport until your check-out time (it prevents you from losing your passport) and when you check out they give a small Paper of Registration together with your passport. All you need to do is to keep this paper safe until your departure.
As a traveler you are responsible for being sure of complying with the legislation of the country you’re visiting!