All foreign citizens visiting Uzbekistan on temporary basis (whether they need visa or not) must submit documents for registration at the place of residence within 72 hours upon arrival to Uzbekistan. Registration is not necessary if you arrive to Uzbekistan during weekend or holidays or if a period of your stay will not exceed three working days. During stay in a hotel your stay will be registered by hotel administration. Upon checking out you should remember of taking the registration form with you stamped by the hotel administration. Registration in Uzbekistan is essential and unavoidable. To enjoy your stay, follow the rules and make sure you are registered.
If you stay in flat or private house then you should be registered via Local Police Department of Registration, so-called (OVIR). Those who issue a Letter of Invitation for you must care about your registration, applying to OVIR for it. This service is chargeable. After filling in necessary forms and paying applicable fees, your passport will be left at the OVIR office for a few days, as it demands a registration process. Just in case keep copy of your passport (make copy of page with an entry visa too) with you at all times.
If you take an overnight train journey, keep the ticket stub or booking confirmation as proof of your whereabouts. If you are camping or staying with friends or at a homestay for more than three nights, you should register at the local OVIR to ensure you (and your hosts) are in the clear.
Punishments for failing to register are applied arbitrarily and you never know if you'll be the unlucky one. Whilst most people will get away with a few missing registration slips (and may not have them checked at all), some unlucky ones could be even detained for couple of days and fined for up to US$1,500 each for failing to register. The requirement for foreigners to register within three days of arriving in any given place is an irritating overhang from the Soviet period and, even more irritatingly, it is often enforced by the authorities. Unless you have plenty of time and money to throw at extricating yourself from the problem, play it safe.
* Please note that it is illegal to stay at private house with tourist visa. You can stay in private house only with business or visitor visas after having special authorization.
Business Visa holders require special authorization to stay in private homes, which should be obtained prior to arrival in Uzbekistan. Ask your inviting business or organization to help you with this. Without such authorization, you will be required to stay in authorized hotels, where they will register you automatically.